Method of presuming domain linker region of protein

ABSTRACT

A domain linker region is predicted by inputting an amino-acid sequence of a protein whose structure is unknown in a hierarchical neural network having identified and learned the domain linker region. Also, the sequence characteristics of the linker domain is identified by a statistical method, and by combining the result with the secondary structure predicting method, a domain linker predicting method for an amino-acid sequence whose structure is unknown was constructed.

FIELD OF THE INVENTION

The present invention relates to a method of learning/predicting/detecting a protein linker sequence by a neural network and more particularly to a method of having the neural network learn a linker sequence in a multi-domain protein, a method of predicting/detecting a linker sequence from amino acid sequence information of the protein, a system for the prediction/detection, a program and a recording media, a method of manufacturing/analyzing a structural domain of a protein, a method of constructing a linker sequence database, a method of constructing a structural domain database, and a peptide having a characteristic sequence pattern in a linker sequence.

BACKGROUND ART

Various individual genomes have been decoded recently, and “structural genome science” has attracted attention as an important study for analysis of systematic structure of a protein using such a large amount of genome sequence information and establishment of correlation between structural functions based on the structure.

In this structural genome study, efficient narrowing of sequences to be analyzed is required by selecting a target which is a typical protein to be coded in a genome and suitable for structural analysis. Suitability for structural determination of a protein largely depends on its molecular weight, and if the current structural determination technology, particularly NMR is used, those for which structural determination can be automated are limited to small proteins with the molecular weight of 20 to 25 thousand. Also, even if there is no technical limitation on NMR or X-ray crystal structure analysis, expression/refinement of a large protein is considerably difficult, especially when unwinding is needed. Thus, when handling a large protein, it is desired that the protein is divided into fragments by domain and each domain is analyzed.

That is, many of proteins with large molecular weights are constituted by combination of a plurality of domains like a module, and it is considered that a variety of functions is realized by the combination. Therefore, in a protein made of such a plurality of domains, quick structural analysis would be possible by dividing it into domains which are its constitutional units and by determining the structure of these domains separately. Also, accurate determination of domain boundaries is important for structural analysis with high resolution or three-dimensional structural modeling, for example.

On the contrary, when determining domain regions, their structural information is unknown in general, and actually, it is extremely difficult to divide a protein into domains correctly under such circumstances.

As a conventional method of dividing a protein into fragments, a protein limited decomposition method by protease, for example, is used experimentally. However, this method requires a great amount of time and labor and can not be effective for systematic, extensive and high-throughput structural analysis.

Thus, how a domain region in a protein can be predicted accurately becomes an important problem in the above-mentioned structural analysis.

In the meantime, there have been many trials to derive information on structure from amino-acid sequences of a protein, and protein structure predicting methods have been developed corresponding to the obtained structural information. The secondary structure of a protein has been most extensively studied structural properties, and methods of predicting the secondary structure have been proposed. These methods are based on physiochemical properties (Lim, 1974; Ptitsyn & Finkelstein, 1983), statistical analysis (Chou & Fasman, 1974; Garnier et al., 1978), pattern matching (Cohen et al., 1983; King & Sternberg, 1990, 1996), neural network (Qian & Sejnowski, 1998; Rost & Sander, 1993), and evolutionarily conserved structure (Zvelebil et al., 1987). In some cases, accuracy of the secondary structural prediction exceeds 70% (Sternberg et al., 1999). The other structural properties such as β structure (Wilmot & Thornton, 1988 ; Shepherd et al., 1999), amino acid on the protein surface (Holbook et al., 1990), center of stabilization (Dosztanyi et al., 1997), and types of structures (Chandonia & Karpus, 1995 ; Chou et al., 1998) have been studied, and their prediction have been examined.

On the contrary, a method of predicting a domain region from an amino-acid sequence has been rarely studied (Busetta & Barrans, 1984; Kikuchi et al., 1988). Except recent several reports (Wheelan et al., 2000 ; Romero et al., 2001), similarity of sequences have been a main method of assuming the location of a domain (Sonnhammer & Kahn, 1994 ; Heinkoff et al., 1997 ; Corpet et al., 1998 ; Kuroda et al., 2001). The methods based on similarity of sequences typically assume that the sequences conserved in various proteins (existing in common) correspond to functional or structural independent bodies and they form a domain.

These methods give useful information on virtual domain in a protein having similar sequences, but they do not intend to detect a property of the sequence to be the characteristics of a structural domain or its boundary.

However, in detecting a property of a sequence of a structural domain, the domain itself is a relatively large structural unit, and extraction of its property becomes complicated, and difficulty in handling has been pointed out.

As a method to solve such a problem, a predicting method is proposed by inventors of the present invention using a neural network focusing attention not to a domain but to a domain linker connecting two domains as structural information (see, for example, S67-1 I 1115, collection of preliminary manuscripts for the 38^(th) annual meeting of the Biophysical Society). According to this method, since a linker sequence is far shorter than a domain sequence, its sequence pattern can be recognized easily.

Also, a method of predicting a domain boundary by a simple statistical method using occurrence frequency of an amino acid in a short range is reported.

However, any of the conventional art remains at a stage for seeking a new method, paying attention to the domain linker, and characteristics of the linker sequence have not been fully extracted. As a result, prediction efficiency is not so high, and it is necessary to characterize a larger segment around the domain boundary in more detail to improve accuracy of the prediction.

Then, according to the present invention, instead of paying attention to the structural domain as structural information, a focus is placed on a domain linker connecting two structural domains, and in fixing a linker sequence, data set for extracting characteristics of sequence pattern of the domain linker is sufficiently examined, accurate information is prepared on the linker sequence, and parameters for prediction are optimized so as to provide a method, a system and a program for predicting and/or detecting a domain linker with more reliability.

DESCRIPTION OF THE INVENTION

The inventors of the present invention employed, in order to identify a sequence connecting two protein domains (linker sequence), a method of having a sequence pattern learned using a neural network and a method of representing an occurrence frequency of an amino-acid residue in a linker domain by score through statistical processing and predicting a linker sequence on a protein whose structure is unknown by combining the both methods in a mutually complementary manner so as to improve prediction efficiency. That is, in the first method, when a domain library defined by SCOP is used to divide into a linker sequence and a non-linker sequence and their respective sequence information is made to be learned separately by the neural network, it was found that there is a great difference in characteristics in amino-acid sequence between the linker and the non-linker domain including an in-domain loop. Also, it was indicated that the linker sequence has a position-dependent preference for an amino acid (Occurrence frequency of a specific amino-acid residue is high at a certain position. The specific amino acid is arranged at the position in preference.) and it was made clear that the fact is not at random. When a domain linker was actually predicted based on such knowledge, a result of a Jackknife test indicated that 58% of a predicted domain matches an actual linker domain (specificity), and 36% of a domain linker derived from SCOP was predicted (sensitivity). This prediction efficiency is more excellent than a simple method derived from a secondary structure prediction, that is, a method which assumes a long loop domain as a virtual domain linker. As a general rule, these results show that a domain linker has a local characteristic different from a loop domain.

Also, in the second method, a domain linker predicting method for an amino-acid sequence whose structure is unknown was constructed by identifying a sequence characteristic of a linker domain in a statistical method and by combining the result with a secondary structure predicting method. That is, a non-redundant sequence set was prepared for a multi-domain protein whose structure is known, a partial sequence having a loop structure was extracted from it and classified into a linker sequence and a non-linker sequence. When the occurrence frequency of each amino-acid residue was examined in each of the sequence sets, it was found out that the occurrence frequency is apparently different between the both in some types of residues. Moreover, in a sequence pattern made of 2 residues, such an example was found that the occurrence frequency was different. The characteristics obtained from these analyses were formulated and a discrimination function was gained that indicates “how much it is like linker” as a score when an arbitrary amino-acid sequence is inputted in the formula. By carrying out secondary structure prediction to a protein whose structure is unknown and by applying this discrimination function to the obtained loop candidates, a position of a domain linker could be predicted at an experimentally effective level. The present invention has been completed based on such knowledge.

The gist of the present invention is as follows.

(1) A method of training a neural network to identify a linker sequence of a protein consisting of 2 or more structural domains comprising:

-   -   a dividing step for dividing an amino-acid sequence of a protein         consisting of 2 or more structural domains of a data set into a         linker sequence and a non-linker sequence;     -   a window setting step for taking a window of a range of 5 to 35         residues within the amino-acid sequence of the protein         consisting of two or more structural domains of the data set;     -   a sequence classifying step in which, if an amino-acid residue         located at the center of the window constitutes a part of the         linker sequence, a numeral value is granted to classify the         amino-acid sequence in the winder as a positive sequence and if         the amino-acid residue located at the center of the window         constitutes a part of the non-linker sequence, a numeral value         is granted to classify the amino-acid sequence in the window as         a negative sequence; and     -   a learning step for repeatedly learning to optimize a weight         parameter of a hierarchical neural network by a back-propagation         method,         in which a value representing an amino-acid sequence in the         window in numerals is input to the hierarchical neural network         to acquire an output value, the error between the output value         and the numeral value which classifies the amino-acid sequence         in the window either as a positive sequence or as a negative         sequence is calculated, and the weight parameter of the         hierarchical neural network is so determined that the error         becomes minimal.

(2) A method of predicting a linker sequence of a protein whose structure is unknown comprising:

-   -   a window setting step for taking a window of a range of 5 to 35         residues within an amino-acid sequence of a protein whose         structure is unknown;     -   an input/output step for obtaining an output value by inputting         a value of the amino-acid sequence in the window represented in         numerals into a hierarchical neutral network having trained by         the method of (1);     -   a predicted value granting step for granting the output value to         an amino-acid residue located at the center of the window as a         predicted value;     -   a step of repeating the input/output step and the predicted         value granting step, with the position of the window being moved         within a desired range of the amino-acid sequence of the protein         whose structure is unknown; and     -   a linker sequence predicting step for predicting as a linker         sequence a region consisting of amino-acid residues with the         predicted values larger than a preset threshold value.

(3) A method as set forth in (2) comprising, following the step of repeating the input/output step and the predicted value granting step:

-   -   an average value calculating step for obtaining an average value         by taking a new window of a range more than the predetermined         number of residues within the amino-acid sequence of the protein         whose structure is unknown and smoothing the predicted values         over the amino-acid residues within this window; and     -   a step for repeating the average value calculating step, with         the position of the new window being moved within a desired         range of the amino-acid sequence of the protein whose structure         is unknown, and in the linker sequence predicting step, a linker         sequence is predicted by the threshold with respect to the         average value of the predicted values.

(4) A method as set forth in (3), wherein in the linker sequence predicting step, if the largest of the predicted values for the amino-acid residues in a region consisting of amino-acid residues whose average value of the predicted values, is larger than a preset threshold value is larger than a preset cut-off value, that region is predicted as a linker sequence.

(5) A system for predicting a linker sequence of a protein whose structure is unknown comprising an amino-acid sequence input means for inputting numerals that represent the amino-acid sequence of the protein whose structure is unknown, a window setting means for taking a window in the amino-acid sequence of the protein whose structure is unknown, an in-window amino-acid sequence input means by which numerals that represent the amino-acid sequence in the window are input into a hierarchical neural network trained to identify the linker sequence of a protein consisting of 2 or more structural domains, an output value calculating means for having the hierarchical neural network calculate an output value, a predicted value granting means for granting the output value to the amino-acid residue located at the center of the window as a predicted value, a window-position moving means for moving the position of the window within a desired range of the amino-acid sequence of the protein whose structure is unknown, a smoothing window setting means for taking a new window of a range more than the predetermined number of residues in the amino-acid sequence of the protein whose structure is unknown, an average value calculating means for obtaining an average value by smoothing predicted values over the amino-acid residues in the new window, a smoothing window moving means for moving the position of the new window within a desired range of the amino-acid sequence of the protein whose structure is unknown, and a linker sequence predicting means for predicting as a linker sequence a region consisting of the amino-acid residues whose average value of the predicted values is larger than a preset threshold value.

(6) A program for having a computer function as a system for predicting a linker sequence of a protein whose structure is unknown characterized in that the system comprises an amino-acid sequence input means for inputting numerals that represent the amino-acid sequence of the protein whose structure is unknown, a window setting means for taking a window in the amino-acid sequence of the protein whose structure is unknown, an in-window amino-acid sequence input means by which numerals that represent the amino-acid sequence in the window are input into a hierarchical neural network trained to identify the linker sequence of a protein consisting of 2 or more structural domains, an output value calculating means for having the hierarchical neural network calculate an output value, a predicted value granting means for granting the output value to the amino-acid residue located at the center of the window as a predicted value, a window-position moving means for moving the position of the window within a desired range of the amino-acid sequence of the protein whose structure is unknown, a smoothing window setting means for taking a new window of a range more than the predetermined number of residues in the amino-acid sequence of the protein whose structure is unknown, an average value calculating means for obtaining an average value by smoothing predicted values over the amino-acid residues in the new window, a smoothing window moving means for moving the position of the new window within a desired range of the amino-acid sequence of the protein whose structure is unknown, and a linker sequence predicting means for predicting as a linker sequence a region consisting of the amino-acid residues whose average value of the predicted values is larger than a preset threshold value.

(7) A computer readable recording medium having recorded thereon a program for having a computer function as a system for predicting a linker sequence of a protein whose structure is unknown characterized in that the system comprises an amino-acid sequence input means for inputting numerals that represent the amino-acid sequence of the protein whose structure is unknown, a window setting means for taking a window in the amino-acid sequence of the protein whose structure is unknown, an in-window amino-acid sequence input means by which numerals that represent the amino-acid sequence in the window are input into a hierarchical neural network trained to identify the linker sequence of a protein consisting of 2 or more structural domains, an output value calculating means for having the hierarchical neural network calculate an output value, a predicted value granting means for granting the output value to the amino-acid residue located at the center of the window as a predicted value, a window-position moving means for moving the position of the window within a desired range of the amino-acid sequence of the protein whose structure is unknown, a smoothing window setting means for taking a new window of a range more than the predetermined number of residues in the amino-acid sequence of the protein whose structure is unknown, an average value calculating means for obtaining an average value by smoothing predicted values over the amino-acid residues in the new window, a smoothing window moving means for moving the position of the new window within a desired range of the amino-acid sequence of the protein whose structure is unknown, and a linker sequence predicting means for predicting as a linker sequence a region consisting of the amino-acid residues whose average value of the predicted values is larger than a preset threshold value.

(8) A method of producing a protein fragment corresponding to one or more structural domains located closer to the N-terminal side than a predicted linker sequence comprising a step for producing at least one of the protein fragments obtained by cutting off a protein at any of the following portions (i), (ii) or (iii):

(i) an arbitrary portion of at least one linker sequence predicted by the method as set forth in any of (2) through (4);

(ii) any of portions located between the C-terminal of at least one linker sequence predicted by the method as set forth in any of (2) through (4) and the 50^(th) amino-acid residue as counted therefrom to the C-terminal side of the protein; or

(iii) any of portions located between the N-terminal of at least one linker sequence predicted by the method as set forth in any of (2) through (4) and the 15^(th) amino-acid residue as counted therefrom to the N-terminal side of the protein.

(9) A method of producing a protein fragment corresponding to one or more structural domains located closer to the C-terminal side than a predicted linker sequence comprising a step for producing at least one of the protein fragments obtained by cutting off a protein at any of the following portions (i), (iv) or (v):

(i) an arbitrary portion of at least one linker sequence predicted by the method as set forth in any of (2) through (4);

(iv) any of portions located between the N-terminal of at least one linker sequence predicted by the method as set forth in any of (2) through (4) and the 50^(th) amino-acid residue as counted therefrom to the N-terminal side of the protein; or

(v) any of portions located between the C-terminal of at least one linker sequence predicted by the method as set forth in any of (2) through (4) and the 15^(th) amino-acid residue as counted therefrom to the C-terminal side of the protein.

(10) A method of analyzing a protein fragment corresponding to one or more structural domains located closer to the N-terminal side than a predicted linker sequence comprising a step for analyzing at least one of the protein fragments obtained by cutting off a protein at any of the following portions (i), (ii) or (iii):

(i) an arbitrary portion of at least one linker sequence predicted by the method as set forth in any of (2) through (4);

(ii) any of portions located between the C-terminal of at least one linker sequence predicted by the method as set forth in any of (2) through. (4) and the 50^(th) amino-acid residue as counted therefrom to the C-terminal side of the protein; or

(iii) any of portions located between the N-terminal of at least one linker sequence predicted by the method as set forth in any of (2) through (4) and the 15^(th) amino-acid residue as counted therefrom to the N-terminal side of the protein.

(11) A method of analyzing a protein fragment corresponding to one or more structural domains located closer to the C-terminal side than a predicted linker sequence comprising a step for analyzing at least one of the protein fragments obtained by cutting off a protein at any of the following portions (i), (iv) or (v):

(i) an arbitrary portion of at least one linker sequence predicted by the method as set forth in any of (2) through (4);

(iv) any of portions located between the N-terminal of at least one linker sequence predicted by the method as set forth in any of (2) through (4) and the 50th amino-acid residue counted therefrom to the N-terminal side of the protein; or

(v) any of portions located between the C-terminal of at least one linker sequence predicted by the method as set forth in any of (2) through (4) and the 15^(th) amino-acid residue as counted therefrom to the C-terminal side of the protein.

(12) A method of constructing a linker sequence database comprising a step for recording in a recording medium the amino-acid sequence data for the linker sequence predicted by the method as set forth in any of (2) through (4).

(13) A method of constructing a structural domain database comprising a step for recording in a recording medium the amino-acid sequence data for the structural domain obtained by cutting off a protein at an arbitrary portion of at least one linker sequence predicted by the method as set forth in any of the (2) through (4).

(14) A peptide which has a sequence pattern satisfying the conditions of (i) and (ii) below and can function as a domain linker of a multi-domain protein:

(i) when a sequence fragment consisting of 19 residues in succession is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε {0,1} (i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit (=19×21) binary sequence obtained as a result of arrangement in series of 21-bit binary sequences associated with amino acid types according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine(G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” in that order and for the 21-bit binary sequence, only those matching the amino acid types of the represented residues are 1, while the others are 0), the value of the following g(x) should be in a range of 0.5 to 1.0: g(x) = τ(v₀ + v₁f₁(x) + v₂f₂(x)) ${f_{j}(x)} = {{\tau\left( {w_{0_{j}} + {\sum\limits_{i = 1}^{399}{w_{ij}x_{i}}}} \right)}\left( {{j = 1},2} \right)}$ τ(u) = 1/(1 + 𝕖^(−u))

-   -   (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and         v_(j)(j=0, 1, 2) is selected from the group consisting of the         combinations of Group 1 in Table A, the combinations of Group 2         in Table B, the combinations of Group 3 in Table C, the         combinations of Group 4 in Table D, the combinations of Group 5         in Table E, the combinations of Group 6 in Table F, the         combinations of Group 7 in Table G, the combinations of Group 8         in Table H, the combinations of group 9 in Table I, and the         combinations of Group 10 in Table J);

(ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 should be included, with an amino acid within 9 residues before and after the central residue being optionally further included.

(15) A method of predicting a region having a sequence pattern satisfying the conditions of (i) and (ii) below as a linker sequence of protein:

(i) when a sequence fragment consisting of 19 residues in succession is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε {0,1} ( i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit, (=19×21) binary sequence obtained as a result of arrangement in series of 21-bit binary sequences associated with amino acid types according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine(G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” in that order and for the 21-bit binary sequence, only those matching the amino acid types of the represented residues are 1, while the others are 0),

-   the value of the following g(x) should be in a range of 0.5 to 1.0:     g(x) = τ(v₀ + v₁f₁(x) + v₂f₂(x))     ${f_{j}(x)} = {{\tau\left( {w_{0_{j}} + {\sum\limits_{i = 1}^{399}{w_{ij}x_{i}}}} \right)}\left( {{j = 1},2} \right)}$     τ(u) = 1/(1 + 𝕖^(−u))     -   (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and         v_(j)(j=0, 1, 2) is selected from the group consisting of the         combinations of Group 1 in Table A, the combinations of Group 2         in Table B, the combinations of Group 3 in Table C, the         combinations of Group 4 in Table D, the combinations of Group 5         in Table E, the combinations of Group 6 in Table F, the         combinations of Group 7 in Table G, the combinations of Group 8         in Table H, the combinations of group 9 in Table I, and the         combinations of Group 10 in Table J);

(ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 should be included, with an amino acid within 9 residues before and after the central residue being optionally further included.

(16) A method of dividing a protein into structural domains characterized in that the protein is cut off at an arbitrary portion of a region having a sequence pattern satisfying the conditions of (i) and (ii) below:

(i) when a sequence fragment consisting of 19 residues in succession is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε {0,1} ( i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit (=19×21) binary sequence obtained as a result of arrangement in series of 21-bit binary sequences associated with amino acid types according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine(G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” in that order and for the 21-bit binary sequence, only those matching the amino acid types of the represented residues are 1, while the others are 0),

-   the value of the following g(x) sould be in a range of 0.5 to 1.0:     g(x) = τ(v₀ + v₁f₁(x) + v₂f₂(x))     ${f_{j}(x)} = {{\tau\left( {w_{0_{j}} + {\sum\limits_{i = 1}^{399}{w_{ij}x_{i}}}} \right)}\left( {{j = 1},2} \right)}$     τ(u) = 1/(1 + 𝕖^(−u))     -   (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and         v_(j)(=0, 1, 2) is selected from the group consisting of the         combinations of Group 1 in Table A, the combinations of Group 2         in Table B, the combinations of Group 3 in Table C, the         combinations of Group 4 in Table D, the combinations of Group 5         in Table E, the combinations of Group 6 in Table F, the         combinations of Group 7 in Table G, the combinations of Group 8         in Table H, the combinations of group 9 in Table I, and the         combinations of Group 10 in Table J);

(ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 should be included, with an amino acid within 9 residues before and after the central residue being optionally further included.

(17) A method of producing a protein fragment comprising a step for producing at least one of the protein fragments obtained by cutting off a protein at an arbitrary portion of a region having a sequence pattern satisfying the conditions of (i) and (ii) below:

(i) when a sequence fragment consisting of 19 residues in succession is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε {0,1} ( i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit (=19×21) binary sequence obtained as a result of arrangement in series of 21-bit binary sequences associated with amino acid types according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine(G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” in that order and for the 21-bit binary sequence, only those matching the amino acid types of the represented residues are 1, while the others are 0),

-   the value of the following g(x) should be in a range of 0.5 to 1.0:     g(x) = τ(v₀ + v₁f₁(x) + v₂f₂(x))     ${f_{j}(x)} = {{\tau\left( {w_{0_{j}} + {\sum\limits_{i = 1}^{399}{w_{ij}x_{i}}}} \right)}\left( {{j = 1},2} \right)}$     τ(u) = 1/(1 + 𝕖^(−u))     -   (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and         v_(j)(j=0, 1, 2) is selected from the group consisting of the         combinations of Group 1 in Table A, the combinations of Group 2         in Table B, the combinations of Group 3 in Table C, the         combinations of Group 4 in Table D, the combinations of Group 5         in Table E, the combinations of Group 6 in Table F, the         combinations of Group 7 in Table G, the combinations of Group 8         in Table H, the combinations of group 9 in Table I, and the         combinations of Group 10 in Table J);

(ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 should be included, with an amino acid within 9 residues before and after the central residue being optionally further included.

(18) A method of analyzing a protein fragment comprising a step for analyzing at least one of the protein fragments obtained by cutting off protein at an arbitrary portion of a region having a sequence pattern satisfying the conditions of (i) and (ii) below:

(i) when a sequence fragment consisting of 19 residues in succession is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε {0,1} ( i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit (=19×21) binary sequence obtained as a result of arrangement in series of 21-bit binary sequences associated with amino acid types according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine(G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” in that order and for the 21-bit binary sequence, only those matching the amino acid types of the represented residues are 1, while the others are 0),

-   the value of the following g(x) should be in a range of 0.5 to 1.0:     g(x) = τ(v₀ + v₁f₁(x) + v₂f₂(x))     ${f_{j}(x)} = {{\tau\left( {w_{0_{j}} + {\sum\limits_{i = 1}^{399}{w_{ij}x_{i}}}} \right)}\left( {{j = 1},2} \right)}$     τ(u) = 1/(1 + 𝕖^(−u))     -   (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and         v_(j)(j=0, 1, 2) is selected from the group consisting of the         combinations of Group 1 in Table A, the combinations of Group 2         in Table B, the combinations of Group 3 in Table C, the         combinations of Group 4 in Table D, the combinations of Group 5         in Table E, the combinations of Group 6 in Table F, the         combinations of Group 7 in Table G, the combinations of Group 8         in Table H, the combinations of group 9 in Table I, and the         combinations of Group 10 in Table J);

(ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 should be included, with an amino acid within 9 residues before and after the central residue being optionally further included.

(19) A method of producing a new multi-domain protein by designing a new linker sequence with a peptide having a sequence pattern satisfying the conditions of (i) and (ii) below and by connecting at least two protein fragments:

(i) when a sequence fragment consisting of 19 in succession is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε {0,1} ( i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit (=19×21) binary sequence obtained as a result of arrangement in series of 21-bit binary sequences associated with amino acid types according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine(G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” in that order and for the 21-bit binary sequence, only those matching the amino acid types of the represented residues are 1, while the others are 0),

-   the value of the following g(x) should be in a range of 0.5 to 1.0:     g(x) = τ(v₀ + v₁f₁(x) + v₂f₂(x))     ${f_{j}(x)} = {{\tau\left( {w_{0_{j}} + {\sum\limits_{i = 1}^{399}{w_{ij}x_{i}}}} \right)}\left( {{j = 1},2} \right)}$     τ(u) = 1/(1 + 𝕖^(−u))     -   (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and         v_(j)(=0, 1, 2) is selected from the group consisting of the         combinations of Group 1 in Table A, the combinations of Group 2         in Table B, the combinations of Group 3 in Table C, the         combinations of Group 4 in Table D, the combinations of Group 5         in Table E, the combinations of Group 6 in Table F, the         combinations of Group 7 in Table G, the combinations of Group 8         in Table H, the combinations of group 9 in Table I, and the         combinations of Group 10 in Table J);

(ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 should be included, with an amino acid within 9 residues before and after the central residue being optionally further included.

(20) A method comprising:

-   i) a step for extracting a linker sequence and a non-linker loop     sequence from a database of multi-domain proteins of known     structures; and -   ii) a step for obtaining, based on statistical processing of     amino-acid sequence of each domain, the probabilities P_(Xaa) ^(L)     and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa)     (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are the probabilities of the     amino-acid residue Xaa occurring in a linker sequence and a     non-linker loop sequence, respectively) and the probabilities     P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of the     amino-acid residues X_(aa) and Y_(aa) as interrupted by m (m is an     integer, m=0, 1, 2) arbitrary amino-acid residues (where     P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are the probabilities of     the amino-acid residues X_(aa) and Y_(aa) occurring in the linker     sequence and the non-linker loop sequence, respectively, as     interrupted by m amino acid residues (the order of X_(aa) and Y_(aa)     does not matter)), said method predicting and/or detecting a linker     sequence in a multi-domain protein of unknown structure from the     characteristics in terms of the amino-acid sequence of the linker     sequence extracted in step i).

(21) A system comprising:

-   i) a means for extracting a linker sequence and a non-linker loop     sequence from a database of multi-domain proteins of known     structures i; and -   ii) a means for obtaining, based on statistical processing of     amino-acid sequence of each domain, the probabilities P_(Xaa) ^(L)     and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa)     (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are the probabilities of the     amino-acid residue X_(aa) occurring in a linker sequence and a     non-linker loop sequence, respectively) and the probabilities     P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of the     amino-acid residues X_(aa) and Y_(aa) as interrupted by m (m is an     integer, m=0, 1, 2) arbitrary amino-acid residues (where     P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are the probabilities of     the amino-acid residues X_(aa) and Y_(aa) occurring in the linker     sequence and then-linker loop sequence, respectively, as interrupted     by m amino acid residues (the order of X_(aa) and Y_(aa) does not     matter)), said system predicting and/or detecting a linker sequence     in a multi-domain protein of unknown structure from the     characteristics in terms of the amino-acid sequence of the linker     sequence extracted by the means of i).

(22) A program for having a computer function as a system for predicting and/or detecting a linker sequence in a multi-domain protein of unknown structure from the characteristics in terms of its amino acid sequence, the system comprising:

-   i) a means for extracting a linker sequence and a non-linker loop     sequence from a database of multi-domain proteins of known     structures; and -   ii) a means for obtaining, based on statistical processing of     amino-acid sequence of each domain, the probabilities P_(Xaa) ^(L)     and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa)     (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are the probabilities of the     amino-acid residue X_(aa) occurring in a linker sequence and a     non-linker loop sequence, respectively) and the probabilities     P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of the     amino-acid residues X_(aa) and Y_(aa) as interrupted by m (m is an     integer, m=0, 1, 2) arbitrary amino-acid residues (where     P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are the probabilities of     the amino-acid residues X_(aa) and Y_(aa) occurring in the linker     sequence and the non-linker loop sequence, respectively, as     interrupted by m amino acid residues (the order of X_(aa) and Y_(aa)     does not matter)).

(23) A structural domain predicting method comprising a step in which a protein fragment generated by cutting off a multi-domain protein of unknown structure at any of the portions of a linker sequence in the multi-domain protein after it was predicted by the method as set forth in (20) is predicted as a structural domain.

(24) A protein producing method comprising a step for producing a protein having the same amino-acid sequence as the structural domain predicted by the method as set-forth in (23).

(25) A protein analyzing method comprising a step for analyzing a protein having the same amino-acid sequence as the structural domain predicted by the method as set forth in (23).

(26) A system for calculating a parameter of an occurrence trend of an amino-acid residue comprising:

-   i) a means for extracting a linker sequence and a non-linker loop     sequence from a database of multi-domain proteins of known     structures; -   ii) a means for obtaining, based on statistical processing of     amino-acid sequence of each domain, the probabilities P_(Xaa) ^(L)     and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa)     (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are the probabilities of the     amino acid residue X_(aa) occurring in a linker sequence and a     non-linker loop sequence, respectively) -   iii) a means for obtaining an occurrence trend parameter S_(Xaa) of     the amino-acid residue X_(aa) by the following equation:     S _(Xaa)=log(P _(Xaa) ^(L) /P _(Xaa) ^(N))

(where S_(Xaa)=0 if there is no statistically significant difference between P_(Xaa) ^(L) and P_(Xaa) ^(N)).

(27) A program for having a computer function as a system for calculating a parameter representing an occurrence trend of an arbitrary amino-acid residue, the system comprising:

-   i) a means for extracting a linker sequence and a non-linker loop     sequence from a database of multi-domain proteins of known     structures; -   ii) a means for obtaining, based on statistical processing of     amino-acid sequence of each domain, the probabilities P_(Xaa) ^(L)     and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa)     (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are the probabilities of the     amino acid residue X_(aa) occurring in a linker sequence and a     non-linker loop sequence, respectively); and -   iii) a means for obtaining an occurrence trend parameter S_(Xaa) of     the amino acid residue X_(aa) by the following equation:     S _(Xaa)=log(P _(Xaa) ^(L) /P _(Xaa) ^(N))     (where S_(Xaa)=0 if there is no statistically significant difference     between P_(Xaa) ^(L) and P_(Xaa) ^(N)).

(28) A system for calculating a parameter of an appearance trend of an amino-acid residue pair comprising:

-   i) a means for extracting a linker sequence and a non-linker loop     sequence from a database of multi-domain proteins of known     structures; -   ii) a means for obtaining, based on statistical processing of amino     acid sequence of each domain, the probabilities P_(XaaYaa(m)) ^(L)     and P_(XaaYaa(m)) ^(N) of occurrence of amino-acid residues X_(aa)     and Y_(aa) (the order of X_(aa) and Y_(aa) does not matter) as     interrupted by m (m is an integer, m=0, 1, 2) arbitrary amino-acid     residues (where P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are the     probabilities of the amino-acid residues X_(aa) and Y_(aa) occurring     (the order of X_(aa) and Y_(aa) does not matter) in a linker     sequence and a non-linker loop sequence, respectively, as     interrupted by m amino-acid residues (m is an integer, m=0, 1, 2))     for the cases where m is 0, 1 and 2, respectively; and -   iii) a means for obtaining an occurrence trend parameter     S_(XaaYaa(m)) of the pair of amino acid residues X_(aa) and Y_(aa)     by the following equation:     S _(XaaYaa(m))=log(P _(XaaYaa(m)) ^(L) /P _(XaaYaa(m)) ^(N))     (where S_(Xaa)=0 if there is no statistically significant difference     between P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N)).

(29) A program for having a computer function as a system for calculating a parameter representing an occurrence trend of an arbitrary amino-acid residue pair, the system comprising:

-   i) a means for extracting a linker sequence and a non-linker loop     sequence from a database of multi-domain proteins of known     structures; -   ii) a means for obtaining, based on statistical processing of amino     acid sequence of each domain, the probabilities P_(XaaYaa(m)) ^(L)     and P_(XaaYaa(m)) ^(N) of occurrence of amino-acid residues X_(aa)     and Y_(aa) (the order of X_(aa) and Y_(aa) does not matter) as     interrupted by m (m is an integer, m=0, 1, 2) arbitrary amino-acid     residues (where P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are the     probabilities of the amino-acid residues X_(aa) and Y_(aa) occurring     (the order of X_(aa) and Y_(aa) does not matter) in a linker     sequence and a non-linker loop sequence, respectively, as     interrupted by m amino-acid residues (m is an integer, m=0, 1, 2))     for the cases where m is 0, 1 and 2, respectively; and -   iii) a means for obtaining an occurrence trend parameter     S_(XaaYaa(m)) of the pair of amino-acid residues X_(aa) and Y_(aa)     by the following equation:     S _(XaaYaa(m))=log(P _(XaaYaa(m)) ^(L) /P _(XaaYaa(m)) ^(N))     (where S_(Xaa)=0 if there is no statistically significant difference     between P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N)).

(30) A system for obtaining a linker degree determination score F₁ for an amino-acid sequence with L₁ amino-acid residues (L₁ is an integer of 1 or more but not more than 21), the system comprising:

-   i) a means for obtaining a linker trend score F₁s of an amino-acid     residue A_(k) by the following equation:     ${F_{1}s} = {\left( {\underset{k = 1}{\overset{L_{i}}{\Sigma}}S_{A\quad k}} \right)/L_{i}}$     (where S_(Ak)=log(P_(Ak) ^(L)/P_(Ak) ^(N)) -   where S_(Ak)=0 if there is no statistically significant difference     between P_(Ak) ^(L) and P_(Ak) ^(N); -   P_(Ak) ^(L) and P_(Ak) ^(N) are the probabilities of the amino-acid     residue A_(k) occurring in a linker sequence and a non-linker loop     sequence, respectively); -   ii) a means for obtaining a linker trend score F₁p of the pair of     amino-acid residues A_(k) and A_(k+(m+1)), as interrupted by m     arbitrary amino-acid residues (m is an integer, m=0, 1, 2), by the     following equation:     ${F_{1}p} = {{\underset{k = 1}{\overset{L_{1}}{\Sigma}}\left( {{\underset{m = 0}{\overset{2}{\Sigma}}\left( {{S_{{AkAk} + {({m + 1})}}(m)} + {S_{{AkAk} + {({m + 1})}}(m)}} \right)}/2} \right)}/L_{1}}$     (where S_(AkAk+(m+1)(m))=log(P_(AkAk+(m+1)(m))     ^(L)/P_(AkAk+(m+1)(m)) ^(N)) and     S_(AkAk−(m+1)(m))=log(P_(AkAk−(m+1)(m)) ^(L)/P_(AkAk−(m+1)(m)) ^(N)) -   where S_(AkAk+(m+1)(m))=0 or S_(AkAk−(m+1)(m))=0 if there is no     statistically significant difference between P_(AkAk+(m+1)(m)) ^(L)     and P_(AkAk+(m+1)(m)) ^(N) or between P_(AkAk−(m+1)(m)) ^(L) and     P_(AkAk−(m+1)(m)) ^(N); -   P_(AkAk+(m+1)(m)) ^(L) and P_(AkAk+(m+1)(m)) ^(N) are the     probabilities of the arbitrary amino-acid residues A_(k) and     A_(k+(m+1)) occurring in a linker sequence and a non-linker loop     sequence, respectively (the order of A_(k) and A_(k+(m+1)) does not     matter), and P_(AkAk−(m+1)(m)) ^(L) and P_(AkAk−(m+1)(m)) ^(N) are     the probabilities of the arbitrary amino-acid residues A_(k) and     A_(k−(m+1)) occurring in the linker sequence and the non-linker loop     sequence, respectively (the order of A_(k) and A_(k−(m+1)) occurring     does not matter)); and -   iii) a means for obtaining a linker degree determination score F₁ by     the following equation below:     F ₁ =F ₁ s+α ₁ F ₁ p     (where 0≦α₁≦1)

(31) A program for having a computer function as a system for obtaining a linker degree determination score F₁ for an amino-acid sequence with L₁ amino-acid residues (L₁ is an integer of 1 or more but not more than 21), the system comprising:

-   i) a means for obtaining a linker trend score F₁s of an amino-acid     residue A_(k) by the following equation:     ${F_{1}s} = {\left( {\underset{k = 1}{\overset{L_{1}}{\Sigma}}S_{Ak}} \right)/L_{1}}$     (where S_(Ak)=log(P_(Ak) ^(L)/P_(Ak) ^(N)) -   where S_(Ak)=0 if there is no statistically significant difference     between P_(Ak) ^(L) and P_(Ak) ^(N); -   P_(Ak) ^(L) and P_(Ak) ^(N) are the probabilities of the amino-acid     residue A_(k) occurring in a linker sequence and a non-linker loop     sequence, respectively); -   ii) a means for obtaining a linker trend score F₁p of the pair of     amino-acid residues A_(k) and A_(k+(m+1)), as interrupted by m     arbitrary amino-acid residues (m is an integer, m=0, 1, 2), by the     following equation:     ${F_{1}p} = {\underset{k = 1}{\overset{L_{1}}{\Sigma}}\left( {{\underset{m = 0}{\overset{2}{\Sigma}}\left( {{S_{{AkAk} + {({m + 1})}}(m)} + {{S_{{AkAk} - {({m + 1})}}(m)}/2}} \right)}/L_{1}} \right)}$     (where S_(AkAk+(m+1)(m))=log(P_(AkAk+(m+1)(m))     ^(L)/P_(AkAk+(m+1)(m)) ^(N)) and     S_(AkAk−(m+1)(m))=log(P_(AkAk−(m+1)(m)) ^(L)/P_(AkAk−(m+1)(m)) ^(N)) -   where S_(AkAk+(m+1)(m))=0 or S_(AkAk−(m+1)(m))=0 if there is no     statistically significant difference between P_(AkAk+(m+1)(m)) ^(L)     and P_(AkAk+(m+1)(m)) ^(N) or between P_(AkAk−(m+1)(m)) ^(L) and     P_(AkAk−(m+1)(m)) ^(N); -   P_(AkAk+(m+1)(m)) ^(L) and P_(AkAk+(m+1)(m)) ^(N) are the     probabilities of the arbitrary amino-acid residues A_(k) and     A_(k+(m+1)) occurring in a linker sequence and a non-linker loop     sequence, respectively (the order of A_(k) and A_(k+(m+1)) does not     matter), and P_(AkAk−(m+1)(m)) ^(L) and P_(AkAk−(m+1)(m)) ^(N) are     the probabilities of the arbitrary amino-acid residues A_(k) and     A_(k−(m+1)) occurring in the linker sequence and the non-linker loop     sequence, respectively (the order of A_(k) and A_(k−(m+1)) does not     matter)); and -   iii) a means for obtaining a linker degree determination score F₁ by     the following equation:     F ₁ =F ₁ s+α ₁ F ₁ p     (where 0≦α₁≦1).

(32) A method of obtaining a linker degree determination score F₁₁(i) for an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) by taking a window of w amino-acid residues before and after the amino-acid residue at the position i (i is an integer of 1 or more but not more than L₂) comprising:

-   i) a step for obtaining a linker trend determination score F₁₁s(i)     of an amino-acid residue A_(k) by the following equation:     ${F_{11}{s(i)}} = {\left( {\sum\limits_{k = {i \cdot w}}^{i + w}S_{Ak}} \right)/W}$     (where W is the window width, and W=2w+1, S_(Ak)=log(P_(Ak)     ^(L)/P_(Ak) ^(N)) -   where S_(Ak)=0 if there is no statistically significant difference     between P_(Ak) ^(L) and P_(Ak) ^(N); -   P_(Ak) ^(L) and P_(Ak) ^(N) are the probabilities of the amino-acid     residue A_(k) occurring in a linker sequence and a non-linker loop     sequence, respectively); -   ii) a step for obtaining the linker trend score F₁₁p(i) of the pair     of amino-acid residues Ai and A_(i+(m+1)), as interrupted by m     arbitrary amino-acid residues (m is an integer, m=0, 1, 2), by the     following equation:     ${F_{11}{p(i)}} = {\sum\limits_{k = {i \cdot w}}^{i + w}{\left( {\sum\limits_{m = 0}^{2}{\left( {{S_{{AiAi} + {({m + 1})}}(m)} + {S_{{AiAi} - {({m + 1})}}(m)}} \right)/2}} \right)/W}}$     (where S_(AiAi+(m+1)(m))=log(P_(AiAi+(m+1)(m))     ^(L)/P_(AiAi+(m+1)(m)) ^(N)) and     S_(AiAi−(m+1)(m))=log(P_(AiAi−(m+P)(m)) ^(L)/P_(AiAi−(m+1)(m)) ^(N)) -   where S_(AiAi+(m+1)(m))=0 or S_(AiAi−(m+1)(m))=0 if there is no     statistically significant difference between P_(AiAi+(m+1)(m)) ^(L)     and P_(AiAi+(m+1)(m)) ^(N) or between P_(AiAi−(m+1)(m)) ^(L) and     P_(AiAi−(m+1)(m)) ^(N); -   P_(AiAi+(m+1)(m)) ^(L) and P_(AiAi+(m+1)(m)) ^(N) are the     probabilities of the pair of the arbitrary amino-acid residues A_(i)     and A_(i+(m+1)) occurring in a linker sequence and a non-linker loop     sequence, respectively (the order of A_(i) and A_(i+(m+i)) does not     matter), and P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N) are     the probabilities of the pair of the arbitrary amino-acid residues     A_(i) and A_(i−(m+i)) occurring in the linker sequence and the     non-linker loop sequence, respectively (the order of A_(i) and     A_(i−(m+1)) does not matter)); and -   iii) a step for obtaining the linker degree determination score     F₁₁(i) of the amino-acid residue Ai at the position i by the     following equation:     F ₁₁(i)=F ₁₁ s(i)+α₁₁ F ₁₁ p(i)     (where 0≦α₁₁≦1).

(33) A system for obtaining a linker degree determination score F₁₁(i) for an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) by taking a window of w amino-acid residues before and after the amino-acid residue at the position i (i is an integer of 1 or more but not more than L₂) comprising:

-   i) a step for obtaining a linker trend determination score F₁₁s(i)     of an amino-acid residue A_(k) by following equation:     ${F_{11}{s(i)}} = {\left( {\sum\limits_{k = {i \cdot w}}^{i + w}S_{Ak}} \right)/W}$     (where W is the window width, and W=2w+1, S_(Ak)=log(P_(Ak)     ^(L)/P_(Ak) ^(N)) -   where S_(Ak)=0 if there is no statistically significant difference     between P_(Ak) ^(L) and P_(Ak) ^(N); -   P_(Ak) ^(L) and P_(Ak) ^(N) are the probabilities of the amino-acid     residue A_(k) occurring in a linker sequence and a non-linker loop     sequence, respectively); -   ii) a step for obtaining the linker trend score F₁₁p(i) of the pair     of amino-acid residues A_(i) and A_(i+(m+1)), as interrupted by m     arbitrary amino-acid residues (m is an integer, m=0, 1, 2), by the     following equation:     ${F_{11}{p(i)}} = {\sum\limits_{k = {i \cdot w}}^{i + w}{\left( {\sum\limits_{m = 0}^{2}{\left( {{S_{{AiAi} + {({m + 1})}}(m)} + {S_{{AiAi}{({m + 1})}}(m)}} \right)/2}} \right)/W}}$     (where S_(AiAi+(m+1)(m))=log(P_(AiAi+(m+1)(m))     ^(L)/P_(AiAi+(m+1)(m)) ^(N)) and     S_(AiAi−(m+1)(m))=log(P_(AiAi−(m+1)(m)) ^(L)/P_(AiAi−(m+1)(m)) ^(N)) -   where S_(AiAi+(m+1)(m))=0 or S_(AiAi−(m+1)(m))=0 if there is no     statistically significant difference between P_(AiAi+(m+1)(m)) ^(L)     and P_(AiAi+(m+1)(m)) ^(N) or between P_(AiAi−(m+1)(m)) ^(L) and     P_(AiAi−(m+1)(m)) ^(N); -   P_(AiAi+(m+1)(m)) ^(L) and P_(AiAi+(m+1)(m)) ^(N) are the     probabilities of the pair of the arbitrary amino-acid residues A_(i)     and A_(i+(m+1)) occurring in a linker sequence and a non-linker loop     sequence, respectively (the order of A_(i) and A_(i+(m+1)) does not     matter), and P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N) are     the probabilities of the pair of the arbitrary amino-acid residues     A_(i) and A_(i−(m+1)) occurring in the linker sequence and the     non-linker loop sequence, respectively (the order of A_(i) and     A_(i−(m+1)) does not matter)); and -   iii) a step for obtaining the linker degree determination score     F₁₁(i) of the amino-acid residue Ai at the position i by the     following equation:     F ₁₁(i)=F ₁₁ s(i)+α₁₁ F ₁₁ p(i)     (where 0≦α₁₁≦1).

(34) A program for having a computer function as a system for obtaining a linker degree determination score F₁₁(i) for an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) by taking a window of w amino-acid residues before and after the amino-acid residue at the position i (i is an integer of 1 or more but not more than L₂), the system comprising:

-   i) a step for obtaining a linker trend score F₁₁s(i) of an     amino-acid residue A_(k) by the following equation:     ${F_{11}{s(i)}} = {\left( {\sum\limits_{k = {i \cdot w}}^{\quad{i + w}}S_{Ak}} \right)/W}$     (where W is the window width, and W=2w+1, S_(Ak)=log(P_(Ak)     ^(L)/P_(Ak) ^(N)) -   where S_(Ak)=0 if there is no statistically significant difference     between P_(Ak) ^(L) and P_(Ak) ^(N); -   P_(Ak) ^(L) and P_(Ak) ^(N) are the probabilities of the amino-acid     residue A_(k) occurring in a linker sequence and a non-linker loop     sequence, respectively); -   ii) a step for obtaining the linker trend score F₁₁ p(i) of the pair     of amino-acid residues A_(i) and A_(i+(m+1)), as interrupted by m     arbitrary amino-acid residues (m is an integer, m=0, 1, 2), by the     following equation:     ${F_{11}{p(i)}} = {\sum\limits_{k = {i \cdot w}}^{i + w}{\left( {\sum\limits_{m = 0}^{2}{\left( {{S_{{AiAi} + {({m + 1})}}(m)} + {S_{{AiAi}{({m + 1})}}(m)}} \right)/2}} \right)/W}}$     (where S_(AiAi+(m+1)(m))=log(P_(AiAi+(m+1)(m))     ^(L)/P_(AiAi+(m+1)(m)) ^(N)) and     S_(AiAi−(m+1)(m))=log(P_(AiAi−(m+1)(m)) ^(L)/P_(AiAi−(m+1)(m)) ^(N)) -   where S_(AiAi+(m+1)(m))=0 or S_(AiAi−(m+1)(m))=0 if there is no     statistically significant difference between P_(AiAi+(m+1)(m)) ^(L)     and P_(AiAi+(m+1)(m)) ^(N) or between P_(AiAi−(m+1)(m)) ^(L) and     P_(AiAi−(m+1)(m)) ^(N); -   P_(AiAi+(m+1)(m)) ^(L) and P_(AiAi+(m+1)(m)) ^(N) are the     probabilities of the pair of the arbitrary amino-acid residues A_(i)     and A_(i+(m+1)) occurring in a linker sequence and a non-linker loop     sequence, respectively (the order of A_(i) and A_(i+(m+1)) does not     matter), and P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N) are     the probabilities of the pair of the arbitrary amino-acid residues     A_(i) and A_(i−(m+1)) occurring in the linker sequence and the     non-linker loop sequence, respectively (the order of A_(i) and     A_(i−(m+1)) does not matter)); and -   iii) a step for obtaining the linker degree determination score     F₁₁(i) of the amino acid residue Ai at the position i by the     following equation:     F ₁₁(i)=F ₁₁ s(i)+α₁₁ F ₁₁ p(i) -   (where 0≦α₁₁≦1).

(35) A method by which a linker degree determination score F₁₂(i) of an amino-acid residue Ai at a position 1 in an amino-acid sequence seq.0 with L₂ amino-acid residues (L₂ is an integer of 22 or more) for which the existence of n homologous sequences seq.1˜seq.n (n is an integer of 1 or more) is known is obtained by taking a window with w amino-acid residues before and after the amino-acid residue at the position i (i is an integer of 1 or more but not more than 22), the method comprising:

-   i) a step for identifying an amino-acid residue A_(i) ^(k) in a     seq.k (k is an integer of 1 or more but not more than n)     corresponding to an amino-acid residue Ai⁰ at a position i in the     seq.0 by aligning seq.0 and seq.1˜seq.n; -   ii) a step for obtaining parameters S′_(Ai), S′_(AiAi+(m+1))(m) and     S′_(AiAi−(m+1))(m) for the amino-acid residue Ai at the position i     by the following equation:     $S_{Ai}^{\prime} = {\left( {\sum\limits_{k = 0}^{n}{S_{Ai}k}} \right)/\left( {n - n_{{gap}\quad 1}} \right)}$     ${S_{{AiAi} + {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}{S_{{{Ai}^{k}{Ai}} + {({m + 1})}^{k}}(m)}} \right)/\left( {n - n_{{gap}\quad 2}} \right)}$     ${S_{{AiAi} - {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}{S_{{{Ai}^{k}{Ai}} - {({m + 1})}^{k}}(m)}} \right)/\left( {n - n_{{gap}\quad 3}} \right)}$     (where n_(gap1) is the number of gaps occurring in A_(i) ^(k),     S_(Ai)k=log(P_(Ai)k^(L)/P_(Ai)k^(N)) -   where S_(Ai)k=0 if there is no statistically significant difference     between P_(Ai)k^(L) and P_(Ai)k^(N); -   P_(Ai)k^(L) and P_(Ai)k^(N)are the probabilities of the amino-acid     residue A_(i) ^(k) occurring in a linker sequence and a non-linker     loop sequence, respectively; -   wherein n_(gap2) is the number of gaps occurring in A_(i) ^(k) or     A_(i+(m+1)) ^(k),     S_(Ai)k_(Ai+(m+1))k(m)=log(P_(Ai)k_(Ai+(m+1))k_((m))     ^(L)/P_(Ai)k_(Ai+(m+1))k_((m)) ^(N)) -   where S_(Ai)k_(Ai+(m+1))k_((m))=0 if there is no statistically     significant difference between P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and     P_(Ai)k_(Ai+(m+1))k_((m)) ^(N); -   P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m)) ^(N)     are the probabilities of the amino-acid residues A_(i) ^(k) and     A_(i+(m+1)) ^(k) occurring in a linker sequence and a non-linker     loop sequence, respectively (the order of A_(i) ^(k) and A_(i+(m+1))     ^(k) does not matter) as interrupted by m arbitrary amino-acid     residues (m is an integer, m=0, 1, 2); -   and wherein n_(gap3) is the number of gaps occurring in A_(i) ^(k)     or A_(i−(m+1)) ^(k),     S_(Ai)k_(Ai−(m+1))k(m)=log(P_(Ai)k_(Ai−(m+1))k_((m))     ^(L)/P_(Ai)k_(Ai−(m+1))k_((m)) ^(N)) -   where S_(Ai)k_(Ai−(m+1))k_((m))=0 if there is no statistically     significant difference between P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and     P_(Ai)k_(Ai−(m+1))k_((m)) ^(N); -   P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m)) ^(N)     are the probabilities of the amino-acid residues A_(i) ^(k) and     A_(i−(m+1)) ^(k) occurring in a linker sequence and a non-linker     loop sequence, respectively (the order of A_(i) ^(k) and A_(i−(m+1))     ^(k) does not matter) as interrupted by m arbitrary amino-acid     residues (m is an integer, m=0, 1, 2)); -   iii) a step for obtaining a linker trend score F₁₂s(i) of an     amino-acid residue by the following equation:     ${F_{12}{s(i)}} = {\left( {\sum\limits_{k = {i \cdot w}}^{i + w}S_{Ak}^{\prime}} \right)/W}$ -   iv) a step for obtaining a linker trend score F₁₂p(i) of an     arbitrary amino-acid residue pair by the following equation:     ${F_{12}{p(i)}} = {\sum\limits_{k = {i \cdot w}}^{i + w}{\left( {\sum\limits_{m = 0}^{2}{\left( {{S_{{AiAi} + {({m + 1})}}^{\prime}(m)} + {S_{{AiAi} - {({m + 1})}}^{\prime}(m)}} \right)/2}} \right)/W}}$     and -   v) a step for obtaining the linker degree determination score F₁₂(i)     for the amino-acid residue Ai at the position i by the following     equation:     F ₁₂(i)=F ₁₂ s(i)+α₁₂ F ₁₂ p(i)     (where 0≦α₁₂≦1).

(36) A system by which a linker degree determination score F₁₂(i) of an amino-acid residue Ai at a position i in an amino-acid sequence seq.0 with L₂ amino-acid residues (L₂ is an integer of 22 or more) for which the existence of n homologous sequences seq.1˜seq.n (n is an integer of 1 or more) is known is obtained by taking a window with w amino-acid residues before and after the amino-acid residue at the position i (i is an integer of 1 or more but not more than 22), the system comprising:

-   i) a means for identifying an amino-acid residue A_(i) ^(k) in a     seq.k (k is an integer of 1 or more but not more than n)     corresponding to an amino-acid residue Ai⁰ at the position i in the     seq.0 by aligning seq.0 and seq.1˜seq.n; -   ii) a means for obtaining parameters for the amino-acid residue Ai     at the position i, S′_(Ai), S′_(AiAi+(m+1))(m) and     S′_(AiAi−(m+1))(m), by the following equation:     $S_{Ai}^{\prime} = {\left( {\sum\limits_{k = 0}^{n}{S_{Ai}k}} \right)/\left( {n - n_{{gap}\quad 1}} \right)}$     ${S_{{AiAi} + {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}{S_{{{Ai}^{k}{Ai}} + {({m + 1})}^{k}}(m)}} \right)/\left( {n - n_{{gap}\quad 2}} \right)}$     ${S_{{AiAi} - {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}{S_{{{Ai}^{k}{Ai}} - {({m + 1})}^{k}}(m)}} \right)/\left( {n - n_{{gap}\quad 3}} \right)}$     (where n_(gap1) is the number of gaps occurring in A_(i) ^(k),     S_(Ai)k=log(P_(Ai)k^(L)/P_(Ai)k^(N)) -   where S_(Ai) ^(k)=0 if there is no statistically significant     difference between P_(Ai)k^(L) and P_(Ai)k^(N); -   P_(Ai)k^(L) and P_(Ai)k^(N) are the probabilities of the amino-acid     residue A_(i) ^(k) occurring in a linker sequence and a non-linker     loop sequence, respectively; -   wherein n_(gap2) is the number of gaps occurring in A_(i) ^(k) or     A_(i+(m+1)) ^(k),     S_(Ai)k_(Ai+(m+1))k_((m))=log(P_(Ai)k_(Ai+(m+1))k_((m))     ^(L)/P_(Ai)k_(Ai+(m+1))k_((m)) ^(N)) -   where S_(Ai)k_(Ai+(m+1))k_((m))=0 if there is no statistically     significant difference between P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and     P_(Ai)k_(Ai+(m+1))k_((m)) ^(N); -   P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m)) ^(N)     are the probabilities of the amino-acid residues A_(i) ^(k) and     A_(i+(m+1)) ^(k) occurring in the linker sequence and the non-linker     loop sequence, respectively (the order of A_(i) ^(k) and A_(i+(m+1))     ^(k) does not matter) as interrupted by m arbitrary amino-acid     residues (m is an integer, m=0, 1, 2); -   and wherein n_(gap3) is the number of gaps occurring in A_(i) ^(k)     or A_(i−(m+1)) ^(k), S_(Ai)k_(Ai−(m+1))k_((m)=log(P)     _(Ai)k_(Ai−(m+1))k_((m)) ^(L)/P_(Ai)k_(Ai−(m+1))k_((m)) ^(N)) -   where S_(Ai)k_(Ai−(m+1))k_((m))=0 if there is no statistically     significant difference between P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and     P_(Ai)k_(Ai−(m+1))k_((m)) ^(N); -   P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m)) ^(N)     are the probabilities of the amino-acid residues A_(i) ^(k) and     A_(i−(m+1))k occurring in the linker sequence and the non-linker     loop sequence, respectively (the order of A_(i) ^(k) and A_(i−(m+1))     ^(k) does not matter) as interrupted by m arbitrary amino acid     residues (m is an integer, m=0, 1, 2)); -   iii) a means for obtaining a linker trend score F₁₂s(i) of an     amino-acid residue by the following equation;     ${F_{12}{s(i)}} = {\left( {\overset{i + w}{\underset{k = {i - w}}{\Sigma}}S_{Ak}^{\prime}} \right)/W}$ -   iv) a means for obtaining a linker trend score F₁₂p(i) of an     arbitrary amino-acid residue pair by the following equation;     ${F_{12}{p(i)}} = {{\underset{k = {i - w}}{\overset{i + w}{\Sigma}}\left( {{\underset{m = 0}{\overset{2}{\Sigma}}\left( {{S_{{AiAi} + {({m + 1})}}^{\prime}(m)} + {S_{{AiAi} - {({m + 1})}}^{\prime}(m)}} \right)}/2} \right)}/W}$     and -   v) a means for obtaining the linker degree determination score     F₁₂(i) for the amino-acid residue Ai at the position i by the     following equation:     F ₁₂(i)=F ₁₂ s(i)+α₁₂ F ₁₂ p(i)     (where 0≦α₁₂≦1).

(37) A program for having a computer function as a system by which a linker degree determination score F₁₂(i) of an amino-acid residue Ai at a position i in an amino-acid sequence seq.0 with L₂ amino-acid residues (L₂ is an integer of 22 or more) for which the existence of n homologous sequences seq.1˜seq.n (n is an integer of 1 or more) is known is obtained by taking a window with w amino-acid residues before and after the amino-acid residue at the position i (i is an integer of 1 or more but not more than 22), the system comprising:

-   i) a means for identifying an amino acid residue A_(i) ^(k) in a     seq.k (k is an integer of 1 or more but not more than n)     corresponding to an amino-acid residue Ai⁰ at the position i in the     seq.0 by aligning seq.0 and seq.1˜seq.n; -   ii) a means for obtaining parameters for the amino-acid residue Ai     at the position i, S′_(Ai), S′_(AiAi+(m+1))(m) and     S′_(AiAi−(m+1))(m), by the following equation: $\begin{matrix}     {S_{Ai}^{\prime} = {\left( {\underset{k = 0}{\overset{n}{\Sigma}}S_{Ai}k} \right)/\left( {n - n_{{gap}\quad 1}} \right)}} \\     {{S_{{AiAi} + {({m + 1})}}^{\prime}(m)} = {\left( {\underset{k = 0}{\overset{n}{\Sigma}}S_{Ai}k_{{Ai} + {({m + 1})}}{k(m)}} \right)/\left( {n - n_{{gap}\quad 2}} \right)}} \\     {{S_{{AiAi} - {({m + 1})}}^{\prime}(m)} = {\left( {\underset{k = 0}{\overset{n}{\Sigma}}S_{Ai}k_{{Ai} - {({m + 1})}}{k(m)}} \right)/\left( {n - n_{{gap}\quad 3}} \right)}}     \end{matrix}$     (where n_(gap1) is the number of gaps occurring in A_(i) ^(k),     S_(Ai)k=log(P_(Ai)k^(L)/P_(Ai)k^(N)) -   where S_(Ai)k=0 if there is no statistically significant difference     between P_(Ai)k^(L) and P_(Ai)k^(N); -   P_(Ai)k^(L) and P_(Ai)k^(N) are the probabilities of the amino-acid     residue A_(i) ^(k) occurring in a linker sequence and a non-linker     loop sequence, respectively; -   wherein n_(gap2) is the number of gaps occurring in A_(i) ^(k) or     A_(i+(m+1)) ^(k),     S_(Ai)k_(Ai+(m+1))k(m)=log(P_(Ai)k_(Ai+(m+1))k_((m))     ^(L)/P_(Ai)k_(Ai+(m+1))k_((m)) ^(N)) -   where S_(Ai)k_(Ai+(m+1))k_((m))=0 if there is no statistically     significant difference between P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and     P_(Ai)k_(Ai+(m+1))k_((m)) ^(N); -   P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m)) ^(N)     are the probabilities of the amino-acid residues A_(i) ^(k) and     A_(i+(m+1)) ^(k) occurring in the linker sequence and the non-linker     loop sequence, respectively (the order of A_(i) ^(k) and A_(i+(m+1))     ^(k) does not matter) as interrupted by m arbitrary amino-acid     residues (m is an integer, m=0, 1, 2); -   and wherein n_(gap3) is the number of gaps occurring in A_(i) ^(k)     or A_(i−(m+1)) ^(k),     S_(Ai)k_(Ai−(m+1))k(m)=log(P_(Ai)k_(Ai−(m+1))k_((m))     ^(L)/P_(Ai)k_(Ai−(m+1))k_((m)) ^(N)) -   where S_(Ai)k_(Ai−(m+1))k_((m))=0 if there is no statistically     significant difference between P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and     P_(Ai)k_(Ai−(m+1))k_((m)) ^(N); -   P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m)) ^(N)     are the probabilities of the amino-acid residues A_(i) ^(k) and     A_(i−(m+1)) ^(k) occurring in the linker sequence and the non-linker     loop sequence, respectively (the order of A_(i) ^(k) and A_(i−(m+1))     ^(k) does not matter) as interrupted by m arbitrary amino-acid     residues (m is an integer, m=0, 1, 2); -   iii) a means for obtaining a linker trend score F₁₂s(i) of an     amino-acid residue by the following equation;     ${F_{12}{s(i)}} = {\left( {\underset{k = {i - w}}{\overset{i + w}{\Sigma}}S_{Ak}^{\prime}} \right)/W}$ -   iv) a means for obtaining a linker trend score F₁₂p(i) of an     arbitrary amino-acid residue pair by the following equation;     ${F_{12}{p(i)}} = {{\underset{k = {i - w}}{\overset{i + w}{\Sigma}}\left( {{\underset{m = 0}{\overset{2}{\Sigma}}\left( {{S_{{AiAi} + {({m + 1})}}^{\prime}(m)} + {S_{{AiAi} - {({m + 1})}}^{\prime}(m)}} \right)}/2} \right)}/W}$     and -   v) a means for obtaining the linker degree determination score     F₁₂(i) for the amino-acid residue Ai at the position i by the     following equation:     F ₁₂(i)=F ₁₂ s(i)+α₁₂ F ₁₂ p(i)     (where 0≦α₁₂≦1).

(38) A method of predicting a domain linker portion comprising:

i) a step for obtaining a linker degree determination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) according to the method as set forth in (32) or (35) (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence);

ii) a step for executing secondary-structure prediction on the amino acid sequence and predicting which regions will take a loop structure;

iii) a step for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker degree determination score is greater than 0; and

iv) a step for predicting for each of the regions obtained in iii) that the position at which the linker degree determination score takes a maximum value is the position at which the domain linker exists.

(39) A system for predicting a domain linker portion comprising:

i) a means for obtaining a linker degree determination score of an amino acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) according to the method as set forth in (32) or (35) (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence);

ii) a means for executing secondary-structure prediction on the amino-acid sequence and predicting which regions will take a loop structure;

iii) a means for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker degree determination score is greater than 0; and

iv) a means for predicting for each of the regions obtained in iii) that the position at which the linker degree determination score takes a maximum value is the position at which the domain linker exists.

(40) A program for having a computer function as a system for predicting a domain linker portion, the system comprising:

i) a means for obtaining a linker degree determination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) according to the method as set forth in (32) or (35) (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence);

ii) a means for executing secondary-structure prediction on the amino-acid sequence and predicting which regions will take a loop structure;

iii) a means for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker degree determination score is greater than 0; and

iv) a means for predicting for each of the regions obtained in iii) that the position at which the linker degree determination score takes a maximum value is the position at which the domain linker exists.

(41) A method of constructing an amino-acid sequence database comprising:

i) a step for obtaining a linker degree determination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) according to the method as set forth in (32) or (35) (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence);

ii) a step for executing secondary-structure prediction on the amino-acid sequence and predicting which regions will take a loop structure;

iii) a step for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker degree determination score is greater than 0;

iv) a step for selecting from the regions obtained in iii) the one whose maximum value of the linker degree determination score is greater than a lower limit value; and

v) a step for recording in a recording medium the amino-acid sequence of the region selected in iv).

(42) A domain linker peptide made of the same amino-acid sequence as the amino-acid sequence of a region whose maximum value of a linker degree determination score is greater than a lower limit value, and which was obtained by a method comprising:

i) a step for obtaining a linker degree determination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino acid residues (L₂ is an integer of 22 or more) according to a method as set forth in (32) or (35) (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino acid sequence);

ii) a step for executing secondary-structure prediction on the amino-acid sequence and predicting which regions will take a loop structure;

iii) a step for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker trend determination score is greater than 0; and

iv) a step for selecting from the regions obtained in iii) the one whose maximum value of the linker degree determination score is greater than the lower limit value.

(43) A method of predicting a structural domain comprising a step for predicting about an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) that a sequence fragment generated by cutting off the amino-acid sequence at any portion of a region including the domain linker portion predicted by the method as set forth in (38) or the position at which a domain linker exists is a structural domain.

(44) A method as set forth in (43), wherein if n domain linker portions are predicted, t of them (t is an integer of 1 or more but not more than n) is selected, all the patterns for cutting an amino acid sequence at that position are considered, and all the sequence fragments obtained are predicted as structural domains.

(45) A system for predicting a structural domain comprising a means for predicting about an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) that a sequence fragment generated by cutting off the amino-acid sequence at any portion of a region including the domain linker portion predicted by the method as set forth in (38) or the position at which a domain linker exists is a structural domain.

(46) A program for having a computer function as a system for predicting a structural domain, the system comprising a means for predicting about an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) that a sequence fragment generated by cutting off the amino-acid sequence at any portion of a region including the domain linker portion predicted by the method as set forth in (38) or the position at which a domain linker exists is a structural domain.

(47) A method of constructing an amino-acid sequence database comprising a step in which concerning an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more), the amino-acid sequence of a sequence fragment generated by cutting off the first-mentioned amino-acid sequence at any portion of a region including the domain linker portion predicted by the method as set forth in (38) or the portion at which a domain linker exists is recorded in a recording medium.

(48) A method of producing a protein comprising a step for producing a protein having the same amino-acid sequence as the structural domain predicted by the method as set forth in (43).

(49) A method of analyzing a protein comprising a step for analyzing a protein having the same amino-acid sequence as the structural domain predicted by the method as set forth in (43).

(50) A method of producing a protein comprising designing a new multi-domain protein generated by connecting at least 2 protein fragments with a domain linker peptide as set forth in (42) and producing this multi-domain protein.

In this description, a “structural domain region” refers to a local region in an amino-acid sequence of a protein, in which a polypeptide chain is folded to form a compact and stable structure. It is needless to say that this polypeptide folding structure is formed in an intact protein, but the structure can also be formed solely or by association with low molecules (ligand, heavy atom, peptide, nucleic acid, etc.) when a structural domain is cut off from a protein.

The “structural domain” means a protein fragment in which a polypeptide chain in a structural domain is folded to form a structure. Since the structural domain can form a structure independently of other portions of a protein, it is also a functionally independent unit in many cases.

A “multi-domain protein” is a protein comprised of two or more structural domains.

A “domain linker” is a sequence taking a loop structure connecting adjacent two structural domains among structures of multi-domain proteins. Usually, the domain linker is a peptide chain shorter than the structural domain.

A “non-linker loop” is a sequence taking a loop structure in a structural domain.

In the fields of structural biology and molecular biology, terms such as “functional domain region” and “functional domain” may be used. The “functional domain region” is a local region in an amino-acid sequence in a protein and a sequence in which a polypeptide chain is folded so as to exert a specific function. It is needless to say that this polypeptide folding structure is formed in an intact protein, but the structure can also be formed solely or by association with low molecules (ligand, heavy atom, peptide, nucleic acid, etc.) when a structural domain is cut off from a protein. The “functional domain” is a protein fragment in which a polypeptide chain of the functional domain region is folded so as to exert a specific function.

The structural domain may solely constitute a functional domain, but a plurality of structural domains may constitute a functional domain. Conversely, it can be said that the functional domain consists of one or more structural domains. Therefore, since the structural domain is a basic structural unit in a structure of a protein, it is also an indispensable unit in analysis of a molecular function of a protein. In the present invention, a relation between an amino-acid sequence not with the functional domain but with the structural domain will be examined.

A “window” is an amino-acid sequence of a certain length (10 residues, for example) in an amino-acid sequence of an intact protein. The window is effective in obtaining characteristics of the residues at the center of the window based on the characteristics of the residues in the region. In a preferred embodiment of the present invention, the window was used for calculating an output value of a neural network and for averaging the output values. Also, in another preferred embodiment of the present invention, the window was used for locally smoothing a numeral value which can be obtained continuously over the full length of a protein.

In this description, “-” indicates a range including numeral values set forth before and after the symbol as a minimum value and a maximum value, respectively.

This description includes specifications and/or drawings in the Japanese Patent Application Nos. 2001-309434 and 2002-172101, underlying the right of priority of the present application.

Brief Description of the Drawings

FIG. 1 shows distribution of average values of neural network output values for a linker sequence and a non-linker sequence. Black and white bar graphs represent distribution of sequence segments corresponding to the linker sequence and the non-linker sequence, respectively. Gray bar graphs represent distribution of in-domain loop sequence. The output values were calculated using a three-layer neural network after learning with the window size of 19 and the number of hidden units of 2 and averaged using a smoothing window of 19 residues (See the section on the smoothing window of Materials & Methods). Averaging of the output values (for positions of the residues in its smoothing window) decreases occurrence of the linker sequence of the average output value at 1.0. For evaluation, a 10-fold Jackknife test was used.

FIG. 2(a) shows a Hinton diagram of optimized weight parameters. The parameter values were shown by positive and negative in red and blue squares, respectively. The parameters were calculated using a neural network without hidden units and explained as contribution of residues for discriminating the domain linker and the non-linker. 10 sets of the independent optimized parameters obtained by the 10-fold Jackknife test were standardized and averaged. We used the window size of 19 residues. (b, c) Proline-rich segments in a domain linker (b) and proline-rich segments inn other regions (c). A sequence of all the segments including at least 3 residues of proline in 9 residues existing in 74 multi-domain proteins (Table 1) (proline-rich segment) is shown. The length of the proline-rich segment is varied from 3 to 9 residues. The praline-rich segment is highlighted, and adjacent 9 residues on both sides are listed in Table. The residues are colored according to contribution in the Hinton diagram (FIG. 2 a). That is, proline is in red, histidine is in blue, and the other amino acids are in white. Identifiers of protein chains are shown on the left with their starting and ending amino-acid residues. The neural network output values smoothed for the proline-rich segment are averaged for the range of the segment and shown on the right. The green hue is in proportion to the output value of the neural network from 0.0 (black) to 1.0 (light green). This value is not shown for the lower row in FIG. 2 c. That is because the proline-rich segment is close to the C terminal of a protein sequence and its smoothed output value could not be obtained. The output value was calculated by the neural network after learning with the window size of 19 and the number of hidden units of 2 and smoothed using the smoothing window of 19 residues.

FIG. 3(a, b) shows efficiency of domain linker prediction by the neural network. The domain linker in a protein sequence was predicted with a threshold value of 0.5. Also, the efficiency predicting the predicted region in the first rank was evaluated using the 10-fold Jackknife test: (a) Cases where the domain linker-corresponding to SCOP derived domain linker (specificity) is predicted. (b) How much share of all the SCOP derived domain linker sequences is held by the SCOP derived domain linker sequences correctly predicted by the neural network (sensitivity). The horizontal axis indicates the size of the smoothing window. The prediction efficiency was obtained using a cut-off value of 0.5 (black circle and bold solid line), 0.7 (white triangle and thin solid line) and 0.9 (while circle and dotted line). (c) Prediction efficiency of domain linker by DSC, PHD. The domain linker was predicted as follows using a secondary structure predicting program. Assume that the loop region predicted by DSC, PHD is ranked based on its length and that a longer loop region has a tendency to become a domain linker, the longest loop region was predicted as a domain linker. As in FIG. 3 a, by changing the length of the loop domain used for prediction, two values (specificity, solid line; sensitivity, broken line) were calculated (horizontal axis). The 10-fold Jackknife test result of production by DSC, PHD is shown with white circles and black squares.

FIG. 4 shows ranking of the predicted domain linkers. The prediction was carried out with the 19-residue smoothing window, threshold value and cut-off value of 0.5 and evaluated using the 10-fold Jackknife test. Occurrence frequency of the linker in the predicted region is shown (black, correct prediction; white wrong prediction). The total of predicted regions was 139, in which 47 corresponded to correct prediction, while 92 were wrong.

FIG. 5 shows a success example of the domain linker prediction. The prediction was carried out with the 19-residue smoothing window, the threshold value and the cut-off value of 0.5. In each example, the lower plot indicates an output value of the neural network (smoothed output value, blue; raw data, light red) against the number of residues. The above diagram shows a ribbon representation (prepared using Molscript and Raster 3D). Here, the predicted domain linker is labeled according to its rank (when two or more regions are predicted), and the regions with boundaries determined by the predicted domain linker were colored to indicate the difference.

FIG. 6 is a failure example of domain linker prediction. The prediction was carried out as in FIG. 5.

FIG. 7 shows a neural network used for sequence classification.

FIG. 8 shows the sequence classification. When a residue at the center of the window is a domain linker, it shall be 0, and when it is not, it shall be 0.

FIG. 9 shows sequence encoding. Each amino-acid residue is represented by a 21-bit binary number. Only the bit at the corresponding residue position is 1, while the others are 0. The 21^(st) bit corresponds to a non-standard amino acid.

FIG. 10 shows a neuron model.

FIG. 11 shows a three-layer neural network.

FIG. 12 is a flow chart for explaining 1 preferred embodiment of how to learn a neural network according to the present invention.

FIG. 13 is a flowchart for explaining 1 preferred embodiment of a method of predicting a linker sequence of a protein according to the present invention.

FIG. 14 is a block diagram showing constitution of a linker sequence predicting system according to the present invention.

FIG. 15 is a block diagram showing functions of a linker sequence predicting system according to the present invention.

FIG. 16 shows distribution of output values of a neural network for residues in and outside a domain linker.

FIG. 17 is a table prepared by extracting a linker sequence portion from a multi-domain protein database with known structure.

FIG. 18 is a table prepared by extracting a linker sequence portion from a multi-domain protein database with known structure.

FIG. 19 a table prepared by extracting a linker sequence portion from a multi-domain protein database with known structure.

FIG. 20 is a flowchart explaining an operation of a linker sequence predicting/detecting system according to a preferred embodiment of the 18^(th) invention of the present application or a preferred embodiment of the 19^(th) invention of the present application.

FIG. 21 is a block diagram showing constitution of a linker sequence predicting/detecting system according to a preferred embodiment of the present invention.

FIG. 22 is a block diagram showing functions of a linker sequence predicting/detecting system according to a preferred embodiment of the 19^(th) invention of the present application.

FIG. 23 is a flowchart of a method of predicting a structural domain according to a preferred embodiment of the 21^(st) invention of the present application.

FIG. 24 is a flowchart explaining an operation of a trend parameter calculating system for a single amino-acid residue according to a preferred embodiment of the 24^(th) invention of the present application.

FIG. 25 is a block diagram explaining functions of a trend parameter calculating system for a single amino-acid residue according to a preferred embodiment of the 24^(th) invention of the present application.

FIG. 26 is a flowchart explaining an operation of a trend parameter calculating system for an amino-acid residue pair according to a preferred embodiment of the 26^(th) invention of the present application.

FIG. 27 is a block diagram explaining functions of a trend parameter calculating system for an amino-acid residue pair according to a preferred embodiment of the 26^(th) invention of the present application.

FIG. 28 is a flowchart explaining an operation of a trend parameter calculating system for an amino-acid residue pair according to a preferred embodiment of the 28^(th) invention of the present application.

FIG. 29 is a block diagram explaining functions of a system for obtaining a linker degree discrimination score F₁s according to a preferred embodiment of the 28^(th) invention of the present application.

FIG. 30 is a flowchart explaining an operation of a system for obtaining a linker degree discrimination score F₂(i) according to a preferred embodiment of the 30^(th) invention of the present application.

FIG. 31 is a block diagram explaining functions of a system for obtaining a linker degree discrimination score F₂(i) according to a preferred embodiment of the 30^(th) invention of the present application.

FIG. 32 is a flowchart explaining an operation of a method of obtaining a linker degree discrimination score F₁₂(i) according to a preferred embodiment of the 33^(rd) invention of the present application or a system for obtaining a linker degree discrimination score F₁₂(i) of the 34^(th) invention of the present application.

FIG. 33 is a block diagram explaining functions of a system for obtaining a linker degree discrimination score F₁₂(i) according to a preferred embodiment of the 34^(th) invention of the present application.

FIG. 34 is a flowchart explaining an operation of a method of predicting a domain linker portion according to a preferred embodiment of the 36^(th) invention of the present application or a predicting system for a domain linker portion according to a preferred embodiment of the 37^(th) invention of the present application.

FIG. 35 is a block diagram explaining functions of a predicting system for a domain linker portion according to a preferred embodiment of the 37^(th) invention of the present application.

FIG. 36 is a flowchart explaining an operation of a method of predicting a domain linker portion according to a preferred embodiment of the 36^(th) invention of the present application or a predicting system for a domain linker portion according to another preferred embodiment of the 37^(th) invention of the present application.

FIG. 37 is a block diagram explaining functions of a predicting system for a domain linker portion according to another preferred embodiment of the 37^(th) invention of the present application.

FIG. 38 is a flowchart explaining an operation of a system for predicting a structural domain according to a preferred embodiment of the 42^(nd) invention of the present application.

FIG. 39 is a block diagram explaining functions of a system for predicting a structural domain according to a preferred embodiment of the 42^(nd) invention of the present application.

FIG. 40 is a flowchart explaining an operation of a system for predicting a structural domain according to another preferred embodiment of the 42^(nd) invention of the present application.

FIG. 41 is a block diagram explaining functions of a system for predicting a structural domain according to another preferred embodiment of the 42^(nd) invention of the present application.

FIG. 42 shows distribution of sequence length.

FIG. 43 shows the length of a sequence (number of amino-acid residues) for each of a linker sequence and a non-linker loop sequence.

FIG. 44 shows a probability of occurrence of an amino-acid residue for each of a linker sequence and a non-linker loop sequence.

FIG. 45 shows how to obtain a single amino-acid residue trend parameter.

FIG. 46 shows grouping and alignment of a linker sequence.

FIG. 47 shows a probability of occurrence of an amino-acid residue pair with 0 piece of an arbitrary amino-acid residue between them for each of a linker sequence and a non-linker loop sequence.

FIG. 48 shows a probability of occurrence of an amino-acid residue pair with 1 piece of an arbitrary amino-acid residue between them for each of a linker sequence and a non-linker loop sequence.

FIG. 49 shows a probability of occurrence of an amino-acid residue pair with 2 pieces of an arbitrary amino-acid residue between them for each of a linker sequence and a non-linker loop sequence.

FIG. 50 shows how to obtain an amino-acid residue pair trend parameter.

FIG. 51 is a distribution map showing distribution state of scores of each sequence by executing a calculation for a linker degree discrimination score according to a preferred embodiment of the 28^(th) invention of the present application for prepared 242 pieces of a linker sequence and 3381 pieces of non-linker sequence with F₁s for the horizontal axis and F₁p for the vertical axis.

FIG. 52 shows a result of domain linker prediction.

FIG. 53 shows how to take a window.

FIG. 54 shows aligned sequences of seq.0 and seq. 1 through seq. n and how to take a window.

FIG. 55 shows an outline of a predicting method of a domain linker portion.

BRIEF DESCRIPTION OF THE NUMERALS

-   1: Computer -   2: CPU -   3: ROM -   4: RAM -   5: Input part -   6: Sending/receiving part -   7: Display part -   8: Hard disk drive -   9: CD-ROM drive -   10: CD-ROM -   11: Amino-acid sequence input part -   12: Window setting part -   13: In-window amino-acid sequence input part -   14: Output value calculation part -   15: Predicted value granting part -   16: Window position moving part -   17: Smoothing window setting part -   18: Average value calculation part -   19: Smoothing window moving part -   20: Linker sequence prediction part -   101: Computer -   102: CPU -   103: ROM -   104: RAM -   105: Input part -   106: Sending/receiving part -   107: Display part -   108: Hard disk drive -   109: CD-ROM drive -   110: CD-ROM -   1021: Linker sequence extraction part -   1022: Non-linker loop sequence extraction part -   1023: P_(Xaa) ^(L) calculation part -   1024: P_(XaaYaa(m)) ^(L) calculation part -   1031: Linker sequence extraction part -   1032: Non-linker loop sequence extraction part -   1033: P_(Xaa) ^(L) calculation part -   1034: P_(XaaYaa(m)) ^(L) calculation part -   1035: S_(Xaa) calculation part -   1041: Linker sequence extraction part -   1042: Non-linker loop sequence extraction part -   1043: P_(Xaa) ^(L) calculation part -   1044: P_(XaaYaa(m)) ^(L) calculation part -   1045: S_(XaaYaa(m)) calculation part -   1051: F₁s calculation part -   1052: F₁p calculation part -   1053: F₁ calculation part -   1071: F₁₁s (i) calculation part -   1072: F₁₁p (i) calculation part -   1073: F₁₁ (i) calculation part -   1081: A_(i) ^(k) identification part -   1082: S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) calculation     part -   1083: F₁₂s (i) calculation part -   1084: F₁₂p (i) calculation part -   1085: F₁₂ (i) calculation part -   1091: F₁₁s (i) calculation part -   1092: F₁₁p (i) calculation part -   1093: F₁₁ (i) calculation part -   1094: Secondary structure prediction part -   1095: Region search part -   1096: Domain linker existing position prediction part -   1101: A_(i) ^(k) identification part -   1102: S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) calculation     part -   1103: F₁₂s (i) calculation part -   1104: F₁₂p (i) calculation part -   1105: F₁₂ (i) calculation part -   1106: Secondary structure prediction part -   1107: Region search part -   1108: Domain linker existing position prediction part -   1201: F₁₁s (i) calculation part -   1202: F₁₁p (i) calculation part -   1203: F₁₁ (i) calculation part -   1204: Secondary structure prediction part -   1205: Region search part -   1206: Domain linker existing position prediction part -   1207: Structural domain prediction part -   1301: A_(i) ^(k) identification part -   1302: S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) calculation     part -   1303: F₁₂s (i) calculation part -   1304: F₁₂p (i) calculation part -   1305: F₁₂ (i) calculation part -   1306: Secondary structure prediction part -   1307: Region search part -   1308: Domain linker existing position prediction part -   1309: Structural domain prediction part

BEST MODE FOR CARRYING-OUT OF THE INVENTION

A suitable mode for carrying out the present invention will be described below referring to the attached drawings. In FIGS. 12, 13, 20, 23, 24, 26, 28, 30, 32, 34, 36, 38 and 40, S indicates each step.

The first invention of the present application is a method of having a neural network identify and learn a linker sequence of a protein consisting of 2 or more structural domains comprising:

a dividing step for dividing an amino-acid sequence of a protein consisting of 2 or more structural domains of a data set into a linker sequence and a non-linker sequence;

a window setting step for taking a window of a range of 5 to 35 residues within the amino-acid sequence of the protein consisting of two or more structural domains of the data set;

a sequence classifying step in which, if an amino-acid residue located at the center of the window constitutes a part of the linker sequence, a numeral value is granted to classify the amino-acid sequence in the window positive sequence and if the amino-acid residue located at the center of the window constitutes a part of the non-linker sequence, a numeral value is granted to classify the amino-acid sequence in the window as a negative sequence; and

a learning step for repeatedly learning to optimize a weight parameter of a hierarchical neural network in a back-propagation method, and the back-propagation method is a method to determine the weight parameter of the hierarchical neural network by inputting a value which represents an amino-acid sequence in the window in a numeral value so as to acquire an output value and by calculating an error between the output value and the numeral value which classifies the amino-acid sequence in the window as a positive sequence or a negative sequence so that the error becomes the minimum.

In the above method, it is advantageous that, before the dividing step for dividing an amino-acid sequence of a protein of a data set into a linker sequence and a non-linker sequence, a data set of an amino-acid sequence of a protein consisting of 2 or more structural domains whose structure is known is created.

In the above method, as a value representing an amino-acid sequence in a numeral value, a numeral value which converted the amino-acid sequence into a binary code can be exemplified. Also, the amino-acid sequence can be represented by a numeral value of 1 when it is classified as a positive sequence, while by a numeral value of 0 when classified as a negative sequence, or these numeral values can be switched (reversed).

The number of hidden units of a neural network may be 0 through 2. In general, the larger this number is, the input/output relations at a higher level can be learned, but when the number of data in a data set is small, the restriction prevents full learning of the high-level correspondence between the amino-acid sequence and structural information, and the effect of setting the number of hidden units to a large number can not be gained. Therefore, in the present invention, for the purpose of decreasing useless variables as much as possible, it is desirable that the range is 0 through 2, but it might become desirable to have a range of 2 or more due to future expansion of the database.

The window size is 5 to 35 amino-acid residues, but more preferably 10 to 35 residues, and furthermore preferably 19 residues. If the window size is less than 5 residues, characteristics of a sequence pattern can not be fully extracted, and full learning effect can not be expected. On the contrary, if it is larger than 35 residues, the number of variables to be determined by learning increases and if the number of learning data is smaller than the number of variables to be determined, “memorization” (phenomenon that even fine characteristics of learning data is extracted) is apt to occur, and learning efficiency tends to degrade.

It is advantageous that the above sequence classifying process and the learning process are repeated by moving the position of the window in a desired range of the amino-acid sequence of a protein of a data set (for example, a range excluding up to 60 residues respectively from the N terminal and the C terminal).

Also, it is advantageous that the above dividing process, window setting process, sequence classifying process and the learning process are executed for the amino-acid sequence of all the proteins in the created data set.

The amino-acid residue located at the center of the window can be an amino-acid residue located in the neighborhood of the center of the window. For example, if the total of the amino-acid residues in a window is 2n+1 pieces, the (n+1)th amino-acid from the 1^(st) amino acid in the window can be cited as an amino-acid residue located at the center of the window, and if the total of the amino-acid residues in a window is 2n pieces, the nth or the (n+1)th amino-acid from the 1^(st) amino acid in the window can be cited as an amino-acid residue located at the center of the window.

The back-propagation method is described in detail in Rumelhalt, 1986.

FIG. 12 is a flow chart for explaining 1 preferred embodiment of how to learn a neural network according to the present invention. Here, a three-layer feed-forward type neural network is used.

First, a data set of amino-acid sequences of proteins whose structure is known and which consists of 2 or more structural domains is prepared. In creating a data set, appropriate protein structures registered in PDB, for example, may be selected.

Each protein in the data set is divided into a linker sequence and a non-linker sequence.

Then, for the protein in the data set, a window is taken in the amino-acid sequence, and if a residue at the center of the window constitutes a part of the linker sequence, the amino-acid sequence in the window is classified as a positive sequence, while a residue at the center of the window constitutes a part of the non-linker sequence, the amino-acid sequence in the window is classified as a negative sequence. This classification process is to be learned by a neural network thereafter, but before that, it is advantageous that input data and teacher data are converted into a binary code. For learning, it is advantageous to use the back-propagation method.

In order to evaluate learning efficiency, the data set is equally divided into the one for training and the other for test. The proportion of the data set for training to the data set for test may be 9:1. In the predicting method by a neural network, the Jackknife method (Chou et al., 1998) can be used as a method for evaluating its prediction efficiency. In this Jackknife method, the data set is divided into 10 groups, in which learning is executed for 9 groups of them, and after tests are made for the rest, this is repeated for all the combinations. By using this method, all the data can be statistically processed as a test data, and even if the number of data sets is small, restriction by the data set number can be overcome. If the number of data sets is sufficient, this method is not necessarily required, and the proportion of training data to test data in evaluating the prediction efficiency can be selected as appropriate. The training data and the test data can be used as fixed or by various combinations. For example, in examining learning conditions, it is advantageous to use the training data and the test data as fixed. Also, once the learning conditions are determined, it is advantageous to make prediction after executing learning with various combinations of training data and test data.

The input data and the teacher data are set (S1). The input data corresponds to an amino-acid sequence in a window taken in the amino-acid sequence of a protein in the data set. The teacher data is correct output to the input data (that is, whether the central residue of the inputted amino-acid sequence constitutes a part of a domain linker or not).

An output signal is obtained from the neural network to which the input data is inputted so as to determine an error from the teacher data (S2).

The error determined in S2 is stored (S3).

It is judged whether the steps of S1 through S3 are carried out for all the training data or not (S4), and if the judgment result is No, the steps of S1 through S3 are carried out for unprocessed training data.

For all the training data, a sum of errors between the output signal and the teacher data is calculated (S5).

By the back-propagation method, a 1-layer and a 2-layer weight parameters (V_(jk), W_(ij)) are updated (S6). $\begin{matrix} {{\Delta\quad{V_{jk}(t)}} = {{{- \Delta}\quad t\quad\underset{x \in X}{\Sigma}{\delta_{2k}(x)}{f_{j}(x)}} + {{\alpha\Delta}\quad{V_{jk}\left( {t - 1} \right)}}}} & (1) \\ {{\Delta\quad{W_{ij}(t)}} = {{{- \Delta}\quad t\quad\underset{x \in X}{\Sigma}{\delta_{1j}(x)}x_{i}} + {{\alpha\Delta}\quad{W_{ij}\left( {t - 1} \right)}}}} & (2) \end{matrix}$ (however, in the above (1), (2) equations, δ_(2k) (x) and δ_(1j) (x) are represented by the following (3), (4) equations, respectively.) $\begin{matrix} {{\delta_{2k}(x)} \equiv {\left\lbrack {{h_{k}(x)} - {d_{k}(x)}} \right\rbrack{h_{k}(x)}\left( {1 - {h_{k}(x)}} \right)}} & (3) \\ {{\delta_{1j}(x)} \equiv {\left\{ {\underset{k = 1}{\overset{1}{\Sigma}}{\delta_{2k}(x)}v_{jk}} \right\}{f_{j}(x)}\left( {1 - {f_{j}(x)}} \right)}} & (4) \end{matrix}$

Then, the learning efficiency is calculated for the test data (S7). For the calculation of the learning efficiency, the test data was inputted in the neural network to obtain an output value, and if the output value (predicted value) of the neural network is not less than 0.5, it was classified as a linker sequence, while if it is 0.5 or less, it was considered to be classified as a non-linker sequence, and its rate of correct answers was calculated:

The calculated value of learning efficiency calculated in S7 is stored (S8).

The weight parameter updated in S6 is stored (S9).

It is judged whether the number of learning steps exceeds a default value or not (S10), and if not, the steps of S1 through S9 are carried out. If the number of learning steps exceeds the default value, the program goes on to S11.

The optimum number of steps with which the calculated value of the learning efficiency becomes the maximum is determined (S11).

The weight parameter at the optimum number of steps is determined as a parameter for prediction (S12). When the training data and the test data are used in various combinations, the optimum number of steps is determined per combination, and parameters for prediction are obtained for the number of combinations. In predicting a linker sequence of a protein, it is advantageous that a series of processing for prediction is executed for each parameter and the obtained prediction results are averaged at the end (Since the prediction results of the neural network is put out in numeral values, these values are averaged.)

It is advantageous that an output device puts out parameters for prediction.

The 2^(nd) invention of the present application provides a method of predicting a linker sequence of a protein whose structure is unknown comprising:

a window setting step for taking a window of a range of 5 to 35 residues within an amino-acid sequence of a protein whose structure is unknown;

an input/output step for obtaining an output value by inputting a value of the amino-acid sequence in the window represented in a numeral value in a hierarchical neutral network having learned in the above method;

a predicted value granting step for granting the output value to an amino-acid residue located at the center of the window as a predicted value;

a step in which the input/output step and the predicted value granting step are repeated by moving the position of the window in a desired range of the amino-acid sequence of the protein whose structure is unknown; and

a linker sequence predicting step for predicting a region made of an amino-acid residue with the predicted value larger than a preset threshold value as a linker sequence.

It is advantageous that, following the step in which the input/output step and the predicted value granting step are repeated, an average value calculating step for obtaining an average value by taking a new window of a range more than a predetermined number of residues within the amino-acid sequence of the protein whose structure is unknown and by smoothing the predicted values among the amino-acid residues within this window; and

a step for repeating the average value calculating step by moving the position of the new window within a desired range of the amino-acid sequence of the protein whose structure is unknown may be included. In this case, in the linker sequence predicting step, it is advantageous that a linker sequence is predicted by the threshold to the average value of the predicted value.

In the above predicting method, a protein whose structure is unknown may be an intact protein or a protein fragment. An amino-acid sequence of a protein is the type and arrangement order of an amino acid constituting the protein (amino-acid sequence).

As an amino-acid sequence of a protein whose structure is unknown, there can be amino-acid sequences of proteins registered in various databases (for example, GeneBank, Protein Data Bank (PDB), SWISSPROT, etc.), amino-acid sequences of newly analyzed proteins, etc.

The “protein whose structure is unknown” shall include those proteins whose structure of the entire range is unknown and those proteins whose part of the structure is known but the rest is unknown.

As a desired range of an amino-acid sequence of a protein whose structure is unknown to move the position of a window, the range excluding up to 60 residues respectively from the N terminal and the C terminal of the protein can be cited, but not limited to that range.

The window size is 5 to 35 amino-acid residues, but more preferably 10 to 35 residues and furthermore preferably 19 residues.

In the above linker sequence predicting method, before the window setting process, a value representing an amino-acid sequence of a protein whose structure is unknown in a numeral value may be inputted.

In the above method, a region made of an amino-acid residue whose average value of predicted values is larger than a threshold value set in advance may be predicted as a linker sequence, and if the largest of the predicted values of the amino-acid residue in a region made of an amino-acid residue whose average value of predicted values is larger than a preset threshold value is larger than a preset cut-off value, the region may be predicted as a linker sequence.

The threshold value is to determine how much allowance is given to the size of a region predicted as a domain linker. If the threshold value is set lower, the size of a predicted region gets larger. If the size of the predicted region gets larger, prediction becomes rough, but the correct answer rate of the prediction is improved.

The cut-off value adjusts specificity (proportion of correct answers in domain linkers predicted by the neural network) and sensitivity (proportion of those which can be predicted by the neural network among actual domain linkers). If the cut-off value is set large, the sensitivity is lowered (that is, domain linkers which can be predicted are limited), but on the contrary, the specificity gets higher (the possibility of correct answer gets high for the predicted regions).

In the predicting method of the present invention, a window is taken in an amino-acid sequence of a given protein, an output value of the neural network for the amino-acid sequence in the window is calculated and the obtained output value (real value in a range of 0.0 to 1.0) is granted as a predicted value of a domain linker trend of the residue at the center of the above window.

Here, since the above output value is relatively easily fluctuated, in order to obtain a prediction result with higher reliability, it is desirable to average the obtained output values. That is, a window for averaging (referred to as a smoothing window) is taken in an amino-acid sequence in the above protein, predicted values granted to each of the amino-acid residues are averaged among the amino-acid residues in this smoothing window, and the obtained average value is made as a predicted value of the domain linker trend of the residue at the center of the above smoothing window.

The size of this smoothing window may only be larger than a predetermined number of residues, for example, not less than 10 amino-acid residues or more preferably, 19 residues. In the range smaller than 10 residues, prediction efficiency is lowered, and linker prediction with high reliability becomes difficult.

In the present invention, based on the averaged predicted value so obtained, in identifying whether the sequence including the amino-acid residue to which this predicted value is given is a domain linker or not, a threshold value and a cut-off value for the predicted value are set and the range larger than set values of the threshold value and the cut-off value is defined as a domain linker. It is preferable that the threshold value and the cut-off value are 0.5 through 1.0. In the range lower than 0.5, the sensitivity for detecting a portion to be a linker sequence can be sufficiently secured but the accuracy (specificity) to be the linker sequence gets lower.

FIG. 13 is a flow chart for explaining 1 preferred embodiment of a method of predicting a linker sequence of a protein according to the present invention.

First, data of an amino-acid sequence of a protein (amino-acid sequence) whose structure is unknown is inputted (S14). The data to be inputted may be, for example, an amino-acid sequence of a protein whose structure is unknown represented in a numeral value.

An output value of a neural network is calculated (S15). When the step of S15 is explained in more detail, a process in which a window is set in an amino-acid sequence of a protein whose structure is unknown, the amino-acid sequence data in the window is inputted in the above hierarchical neural network having learned and an output value is calculated is carried out for all the window positions. The output value of the neural network is granted to its central residue as a predicted value indicating whether the residue at the center of the amino-acid sequence in the window constitutes a part of a linker sequence or not.

Then, the predicted value is averaged among amino-acid residues in the smoothing window (averaging window) (S16). The smoothing window is a new window set in the amino-acid sequence of the protein whose structure is unknown for averaging the predicted value. The position of this smoothing window is moved within a desired range in the amino-acid sequence of the protein whose structure is unknown so as to average the predicted value.

A region made of an amino-acid residue whose average value is larger than the threshold value is determined (S17).

A region where the largest average value of the predicted values of the amino-acid residues in the region determined in S17 is larger than a cut-off value is made as a linker sequence (S18). Or the region determined in S17 may be the linker sequence.

It is advantageous that the linker sequence is outputted to an output device.

The 3^(rd) invention of the present application is a system for predicting a linker sequence of a protein whose structure is unknown (hereinafter referred to as “linker sequence predicting system”) comprising an amino-acid sequence input means for inputting a value of the amino-acid sequence of the protein whose structure is unknown represented in a numeral value, a window setting means for taking a window in the amino-acid sequence of the protein whose structure is unknown, an in-window amino-acid sequence input means for inputting the value of the amino-acid sequence in the window represented in a numeral value into a hierarchical neural network having identified and learned the linker sequence of the protein consisting of 2 or more structural domains, an output value calculating means for having the hierarchical neural network calculate an output value, a predicted value granting means for granting the output value to the amino-acid residue located at the center of the window as a predicted value, a window-position moving means for moving the position of the window in a desired range of the amino-acid sequence of the protein whose structure is unknown, a smoothing window setting means for taking a new window of a range more than the predetermined number of residues in the amino-acid sequence of the protein whose structure is unknown, an average value calculating means for obtaining an average value by smoothing predicted values among the amino-acid residues in the new window, a smoothing window moving means for moving the position of the new window within a desired range of the amino-acid sequence of the protein whose structure is unknown, and a linker sequence predicting means for predicting a region consisting of the amino-acid residues with the average value of the predicted value larger than a preset threshold value as a linker sequence.

The window size is 5 to 35 amino-acid residues, but more preferably 10 to 35 residues, and furthermore preferably 19 residues.

The size of the new window may be not less than the predetermined number of residues, for example, not less than 10 amino-acid residues and more preferably 19 residues.

As a hierarchical neural network having identified and learned a linker sequence of a protein consisting of 2 or more structural domains, a neural network having learned by the method of the first invention of the present application is preferable.

As a desired range of an amino-acid sequence of a protein whose structure is unknown in which the position of the window and the smoothing window are to be moved, the range excluding up to 60 residues from the N terminal and the C terminal respectively of the protein can be cited, but not limited to that range.

The 4^(th) invention of the present application provides a program for having a computer function as a system for predicting a linker sequence of a protein whose structure is unknown characterized in that the system comprises an amino-acid sequence input means for inputting a value of the amino-acid sequence of the protein whose structure is unknown represented in a numeral value, a window setting means for taking a window in the amino-acid sequence of the protein whose structure is unknown, an in-window amino-acid sequence input means for inputting the value of the amino-acid sequence in the window represented in a numeral value into a hierarchical neural network having identified learned the linker sequence of the protein consisting of 2 or more structural domains, an output value calculating means for having the hierarchical neural network calculate an output value, a predicted value granting means for granting the output value to the amino-acid residue located at the center of the window as a predicted value, a window-position moving means for moving the position of the window in a desired range of the amino-acid sequence of the protein whose structure is unknown, a smoothing window setting means for taking a new window of a range more than the predetermined number of residues in the amino-acid sequence of the protein whose structure is unknown, an average value calculating means for obtaining an average value by smoothing predicted values among the amino-acid residues in the new window, a smoothing window moving means for moving the position of the new window within a desired range of the amino-acid sequence of the protein whose structure is unknown, and a linker sequence predicting means for predicting a region consisting of the amino-acid residues with the average value of the predicted value larger than a preset threshold value as a linker sequence.

The 5^(th) invention of the present application provides a computer readable recording medium which recorded a program for having a computer function as a system for predicting a linker sequence of a protein whose structure is unknown characterized in that the system comprises an amino-acid sequence input means for inputting a value of the amino-acid sequence of the protein whose structure is unknown represented in a numeral value, a window setting means for taking a window in the amino-acid sequence of the protein whose structure is unknown, an in-window amino-acid sequence input means for inputting the value of the amino-acid sequence in the window represented in a numeral value into a hierarchical neural network having identified and learned the linker sequence of the protein consisting of 2 or more structural domains, an output value calculating means for having the hierarchical neural network calculate an output value, a predicted value granting means for granting the output value to the amino-acid residue located at the center of the window as a predicted value, a window-position moving means for moving the position of the window in a desired range of the amino-acid sequence of the protein whose structure is unknown, a smoothing window setting means for taking a new window of a range more than the predetermined number of residues in the amino-acid sequence of the protein whose structure is unknown, an average value calculating means for obtaining an average value by smoothing predicted values among the amino-acid residues in the new window, a smoothing window moving means for moving the position of the new window within a desired range of the amino-acid sequence of the protein whose structure is unknown, and a linker sequence predicting means for predicting a region consisting of the amino-acid residues with the average value of the predicted value larger than a preset threshold value as a linker sequence.

This recording medium which recorded the program may be ROM itself of the linker sequence predicting system or CD-ROM or the like which can be read when the recording medium is inserted into a program reading device such as a CD-ROM drive provided as an external memory unit. Or the above recording medium may be a magnetic tape, cassette tape, flexible disk, hard disk, MO/MD/DVD, etc. or semiconductor memory.

FIG. 14 is a block diagram showing constitution of a linker sequence predicting system according to the present invention. This system comprises a computer 1 provided with a CPU 2, a ROM 3, a RAM 4, an input part 5, a sending/receiving part 6, a display part 7, a hard disk drive 8 and a CD-ROM drive 9. Instead of a CD-ROM 10, a rewritable CD-R or CD-RW can be used as a recording medium. In that case, instead of the CD-ROM drive 9, a drive for CD-R or for CD-RW is provided. Instead of the CD-ROM 10, DVD, ZiP, MO, PD and their media can be used as a medium for maintaining information and a drive corresponding to it can be provided.

The CPU 2 controls the entire linker sequence predicting system according to the program stored in the ROM 3, the RAM 4 or the hard disk drive (HDD) 8 and executes the linker sequence predicting processing which will be described later. The ROM 3 stores programs and so on for commanding processing required for operation of the linker sequence predicting system. The RAM 4 temporarily stores data required for execution of the linker sequence predicting processing. The input part 5 includes a keyboard, mouse, etc. manipulated when inputting conditions necessary for execution of the linker sequence predicting system. The sending/receiving part 6 executes sending/receiving processing of data through a communication line based on the command of the CPU 2. The display part 7 executes processing for displaying input information, output information, etc. based on the command from the CPU 2. The hard disk drive (HDD) 8 stores the linker sequence predicting program, data sets, etc., reads out the stored program, data sets, etc. based on the command of the CPU 2 and stores them in the RAM 43, for example, The CD-ROM drive 9 reads out a program, data or the like from the stored program, data sets, etc. stored in the CD-ROM 10 based on the command of the CPU 2 and stores them in the hard disk drive (HDD) 8, for example,

FIG. 15 is a block diagram explaining functions of the linker sequence predicting system according to the present invention. To an amino-acid sequence input part 11, a value representing an amino-acid sequence of a protein whose structure is unknown in a numeral value is inputted. In a window setting part 12, a window is set in an amino-acid sequence of a protein whose structure is unknown. In an in-window amino-acid sequence input part 13, a value representing an amino-acid sequence in the window in a numeral value is inputted into a hierarchical neural network having identified and learned a linker sequence of a protein consisting of 2 or more structural domains. In an output value calculation part 14, an output value is calculated by the hierarchical neural network. At a predicted value granting part 15, the output value is granted as a predicted value to an amino-acid residue located at the center of the window. In a window position moving part 16, the position of a window is moved in a desired range of the amino-acid sequence of the protein whose structure is unknown. In a smoothing window setting part 17, a new window in a range larger than the predetermined number of residues is set in the amino-acid sequence of the protein whose structure is unknown. In an average value calculation part 18, a predicted value is averaged among the amino-acid residues in the new window so as to obtain an average value. In a smoothing window moving part 19, the position of the new window is moved in a desired range of the amino-acid sequence of the protein whose structure is unknown. In a linker sequence prediction part 20, a region consisting of an amino-acid residue whose average value of the predicted value is larger than a preset threshold value is predicted as a linker sequence.

The 6^(th) invention of the present application provides a method of producing a protein fragment corresponding to one or more structural domains located on the side of an N-terminal from a predicted linker sequence comprising a step for producing at least one of the protein fragments obtained by cutting off a protein at any of the following portions (i), (ii) or (iii):

(i) an arbitrary portion of at least one linker sequence predicted by the above method;

(ii) any of portions located between a C-terminal of at least one linker sequence predicted by the above method and the 50^(th) amino-acid residue counted therefrom to the C-terminal side of the protein; or (iii) any of portions located between the N-terminal of at least one linker sequence predicted by the above method and the 15^(th) amino-acid residue counted therefrom to the N-terminal side of the protein.

By this method, a protein can be cut off without breaking the structure of a structural domain existing on the side of the N terminal of the predicted linker sequence so as to obtain a protein fragment.

The above (ii) portion exists between the C terminal of at least one linker sequence predicted by the above method and the 50^(th) amino-acid residue counted therefrom to the C-terminal side of the protein, but preferably existing between the C terminal of the linker sequence and the 30^(th) amino-acid residue counted therefrom to the C-terminal side of the protein.

Also, the above (iii) portion exists between the N terminal of at least one linker sequence predicted by the above method and the 15^(th) amino-acid residue counted therefrom to the N-terminal side of the protein, but preferably existing between the N terminal of the linker sequence and the 10^(th) amino-acid residue counted therefrom to the N-terminal side of the protein.

The 7^(th) invention of the present application provides a method of producing a protein fragment corresponding to one or more structural domains located on the side of a C-terminal from a predicted linker sequence comprising a step for producing at least one of the protein fragments obtained by cutting off a protein at any of the following portions (i), (iv) or (v):

(i) an arbitrary portion of at least one linker sequence predicted by the above method;

(iv) any of portions located between an N-terminal of at least one linker sequence predicted by the above method and the 50^(th) amino-acid residue counted therefrom to the N-terminal side of the protein; or

(v) any of portions located between the C-terminal of at least one linker sequence predicted by the above method and the 15^(th) amino-acid residue counted therefrom to the C-terminal side of the protein.

By this method, a protein can be cut off without breaking the structure of a structural domain existing on the side of the C terminal of the predicted linker sequence so as to obtain a protein fragment.

The above (iv) portion exists between the N terminal of at least one linker sequence predicted by the above method and the 50^(th) amino-acid residue counted therefrom to the N-terminal side of the protein, but preferably existing between the N terminal of the linker sequence and the 30^(th) amino-acid residue counted therefrom to the N-terminal side of the protein.

Also, the above (v) portion exists between the C terminal of at least one linker sequence predicted by the above method and the 15^(th) amino-acid residue counted therefrom to the C-terminal side of the protein, but preferably existing between the C terminal of the linker sequence and the 10^(th) amino-acid residue counted therefrom to the C-terminal side of the protein.

For manufacture of a protein fragment, any publicly known method, that is, a chemical synthesizing method, genetic engineering method, etc. may be used.

The 8^(th) invention of the present application provides a method of analyzing a protein fragment corresponding to one or more structural domains located on the side of an N-terminal from a predicted linker sequence comprising a step for analyzing at least one of the protein fragments obtained by cutting off a protein at any of the following portions (i), (ii) or (iii):

(i) an arbitrary portion of at least one linker sequence predicted by the above method;

(ii) any of portions located between a C-terminal of at least one linker sequence predicted by the above method and the 50^(th) amino-acid residue counted therefrom to the C-terminal side of the protein; or

(iii) any of portions located between the N-terminal of at least one linker sequence predicted by the above method and the ₁₅ ^(th) amino-acid residue counted therefrom to the N-terminal side of protein.

By this method, a protein can be cut off without breaking the structure of a structural domain existing on the side of the N terminal of the predicted linker sequence so as to analyze the structure of a protein fragment.

The above (ii) portion exists between the C terminal of at least one linker sequence predicted by the above method and the 50^(th) amino-acid residue counted therefrom to the C-terminal side of the protein, but preferably existing between the C terminal of the linker sequence and the 30^(th) amino-acid residue counted therefrom to the C-terminal side of the protein.

Also, the above (ii) portion exists between the N terminal of at least one linker sequence predicted by the above method and the 15^(th) amino-acid residue counted therefrom to the N-terminal side of the protein, but preferably existing between the N terminal of the linker sequence and the 10^(th) amino-acid residue counted therefrom to the N-terminal side of the protein.

The 9^(th) invention of the present application provides a method of analyzing a protein fragment corresponding to one or more structural domains located on the side of a C-terminal from a predicted linker sequence comprising a step for analyzing at least one of the protein fragments obtained by cutting off a protein at any of the following portions (i), (iv) or (v):

(i) an arbitrary portion of at least one linker sequence predicted by the above method;

(iv) any of portions located between an N-terminal of at least one linker sequence predicted by the above method and the 50^(th) amino-acid residue counted therefrom to the N-terminal side of the protein; or

(v) any of portions located between the C-terminal of at least one linker sequence predicted by the above method and the 15^(th) amino-acid residue counted therefrom to the C-terminal side of the protein.

By this method, a protein can be cut off without breaking the structure of a structural domain existing on the side of the C terminal of the predicted linker sequence so as to analyze the structure of a protein fragment.

The above (iv) portion exists between the N terminal of at least one linker sequence predicted by the above method and the 50^(th) amino-acid residue counted therefrom to the N-terminal side of the protein, but preferably existing between the N terminal of the linker sequence and the 30^(th) amino-acid residue counted therefrom to the N-terminal side of the protein.

Also, the above (v) portion exists between the C terminal of at least one linker sequence predicted by the above method and the 15^(th) amino-acid residue counted therefrom to the N-terminal side of the protein, but preferably existing between the C terminal of the linker sequence and the 10^(th) amino-acid residue counted therefrom to the C-terminal side of the protein.

As analysis of a protein fragment, in addition to the X-ray crystal structure analysis, protein structure analysis by NMR, etc., measurement of various bioactivities can be cited.

In the above manufacture/analyzing methods of a protein fragment, the protein fragment is a concept including a structural domain.

In order to cut off a protein, any publicly known method, that is, an enzymic method using protease, chemical decomposition method to cut off a peptide chain using chemicals, etc. may be used.

The 10^(th) invention of the present application provides a method of constructing a linker sequence database comprising a step for recording amino-acid sequence data of the linker sequence predicted by the above method in a recording medium.

The 11^(th) invention of the present application provides a method of constructing a structural domain database comprising a step for recording amino-acid sequence data of the structural domain obtained by cutting off a protein at an arbitrary portion of at least one linker sequence predicted by the above method in a recording medium.

As a recording medium, a magnetic tape, cassette tape, flexible disk, hard disk, MO/MD/DVD, etc. or semiconductor memory can be cited.

The 12^(th) invention of the present application provides a peptide which has a sequence pattern satisfying the conditions of (i) and (ii) below and can function as a domain linker of a multi-domain protein:

(i) when a sequence fragment consisting of continuous 19 residues is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε {0,1} (i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit (=19×21) binary sequence obtained as a result of arrangement in a series of 21-bit binary sequences corresponding to the type of an amino acid according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to, in order, “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine(G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” and for the 21-bit binary sequence, only those matching the type of the amino acid of the represented residues are 1, while the others are 0.)

-   the value of the following g(x) is in a range of 0.5 to 1.0.     $\begin{matrix}     {{g(x)} = {\tau\left( {v_{0} + {v_{1}{f_{1}(x)}} + {v_{2}{f_{2}(x)}}} \right)}} \\     {{f_{j}(x)} = {{\tau\left( {w_{0\quad j} + {\sum\limits_{i = 1}^{399}{w_{ij}x_{i}}}} \right)}\left( {{j = 1},2} \right)}} \\     {{\tau(u)} = {1/\left( {1 + {\mathbb{e}}^{- u}} \right)}}     \end{matrix}$     -   (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and         v_(j)(j=0, 1, 2) is selected from a group consisting of a         combination of Group 1 in Table A, a combination of Group 2 in         Table B, a combination of Group 3 in Table C, a combination of         Group 4 in Table D, a combination of Group 5 in Table E, a         combination of Group 6 in Table F, a combination of Group 7 in         Table G, a combination of Group 8 in Table H, a combination of         group 9 in Table I, and a combination of Group 10 in Table J.)

(ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 may be included, and an amino acid within 9 residues before and after the central residue may further be included.

The above peptide may consist only of the sequence pattern satisfying the conditions in the above (i) and (ii) or may include other amino-acid sequences as long as it can function as a domain linker of a multi-domain protein.

The range of the numeral values of g(x) is preferably 0.5-1.0. If the value is lower than 0.5, prediction accuracy is lowered and it causes a problem in reliability.

The 13^(th) invention of the present application provides a method of predicting a region having a sequence pattern satisfying the conditions of the above (i) and (ii) as a linker sequence of protein. For example, by detecting a sequence pattern satisfying the conditions of the above (i) and (ii) from amino-acid sequences of proteins registered in various databases (for example, GeneBank, PDB, SWISSPROT, etc.), amino-acid sequences of newly analyzed proteins, etc., a region having the sequence pattern can be predicted as a linker sequence.

The 14^(th) invention of the present application provides a method of dividing a protein into structural domains characterized in that the protein is cut off at an arbitrary portion of a region having a sequence pattern satisfying the conditions of the above (i) and (ii).

In order to cut off a protein, any publicly known method, that is, an enzymic method using protease, chemical decomposition method to cut off a peptide chain using chemicals, etc. may be used.

The 15^(th) invention of the present application provides a method of producing a protein fragment comprising a step for producing at least one of the protein fragments obtained by cutting off a protein at an arbitrary portion of a region having a sequence pattern satisfying the conditions of the above (i) and (ii).

For manufacture of a protein fragment, any publicly known method, that is, a chemical synthesizing method, genetic engineering method, etc. may be used.

The 16^(th) invention of the present application provides a method of analyzing a protein fragment comprising a step for analyzing at least one of the protein fragments obtained by cutting off protein at an arbitrary portion of a region having a sequence pattern satisfying the conditions of the above (i) and (ii)

As analysis of a protein fragment, in addition to the X-ray crystal structure analysis, protein structure analysis by NMR, etc., measurement of various bioactivities can be cited.

In the above manufacture/analyzing methods of a protein fragment, the protein fragment is a concept including a structural domain.

In order to cut off a protein, any publicly known method, that is, an enzymic method using protease, chemical decomposition method to cut off a peptide chain using chemicals, etc. may be used.

The 17^(th) invention of the present application provides a method of producing a new multi-domain protein by designing a new domain linker using a peptide having a sequence pattern satisfying the conditions of the above (i) and (ii) and by connecting at least two protein fragments.

For manufacture of a protein fragment, any publicly known method, that is, a chemical synthesizing method, genetic engineering method, etc. may be used.

The 18^(th) invention of the present application provides a method of predicting and/or detecting a linker sequence in a multi-domain protein sequence whose structure is unknown from characteristics of the above linker sequence on an amino-acid sequence comprising:

i) a step for extracting a linker sequence and a non-linker loop sequence from a database of multi-domain protein whose structure is known; and

ii) a step for obtaining, based on statistical processing of amino-acid sequence of each domain, probabilities P_(Xaa) ^(L) and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa) (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are probabilities of occurrence of the amino-acid residue X_(aa) in a linker sequence and a non-linker loop sequence, respectively) and probabilities P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of the amino-acid residues X_(aa) and Y_(aa) with m pieces (m is an integer, m=0, 1, 2) of arbitrary amino-acid residues between them (where P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are probabilities of occurrence of the amino-acid residues X_(aa) and Y_(aa) in the linker sequence and the non-linker loop sequence, respectively, with m pieces of amino acid residues between them (the order of X_(aa) and Y_(aa) does not matter)).

In the 18^(th) invention of the present application, the above multi-domain protein database whose structure is known provides both amino-acid sequences and structural coordinates of a protein. They are created by, for example, open databases such as SCOP, nr-PDB, etc. Also, as an example of a selecting method, DSSP, Visual inspection can be cited, but not limited to them.

In the 18^(th) invention of the present application, a linker sequence and a non-linker loop sequence are extracted from the above multi-domain protein database whose structure is known, and an amino-acid sequence corresponding to each region is used as a data set.

FIGS. 17 through 19 show an example of so extracted linker sequences. As shown in Table of FIG. 17, it is advantageous to prepare PDB chain, length, position of the linker sequence, name of the protein, etc. as a data set.

On the other hand, the above non-linker loop sequence is a loop sequence in the above multi-domain protein database whose structure is known from which the above linker sequence and regions located at both N/C terminals are removed.

When extracting these linker sequences and non-linker loop sequences, the following standard can be used.

First, a loop sequence with the length indicated by DSSP or the like of 4 residues or more is extracted. Those including a domain boundary defined by the open database such as SCOP in this loop region or at the terminal of the loop sequence are classified as a linker sequence, while those other than the linker sequence and not located at either of the N/C terminals are classified as a non-linker loop sequence.

Also, based on statistical processing of amino-acid sequence of the above linker sequence and the above non-linker loop sequence, probabilities P_(Xaa) ^(L) and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa) and probabilities P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of the amino-acid residues X_(aa) and Y_(aa) with m pieces (m is an integer, m=0, 1, 2) of arbitrary amino-acid residues between them can be obtained as follows.

First, when the total number of amino-acid residues included in an amino-acid sequence of a target linker sequence (or a non-linker loop sequence) is N_(total) and an occurrence frequency of an amino-acid residue X_(aa) in the amino-acid sequence is N_(Xaa), P _(Xaa) ^(L) =N _(Xaa) /N _(total) (P _(Xaa) ^(N) =N _(Xaa) /N _(total))

Also, when all the partial sequence patterns of the length m+2 (m is an integer, m=0, 1, 2) included in the amino-acid sequence of the target linker sequence (or the non-linker loop sequence) is N_(total(m)) and the occurrence frequency of the amino-acid residues X_(aa) and Y_(aa) in the amino-acid sequence with m pieces of arbitrary amino-acid residues between them (the order of X_(aa) and Y_(aa) does not matter) is N_(XaaYaa(m)), P _(XaaYaa(m)) ^(L) =N _(XaaYaa(m)) /N _(total(m)) (P _(XaaYaa(m)) ^(N) =N _(XaaYaa(m)) /N _(total(m)))

These P_(Xaa) ^(L) and P_(XaaYaa(m)) ^(L) (or P_(Xaa) ^(N) and P_(XaaYaa(m)) ^(N))can be used for predicting/detecting a linker sequence in the multi-domain protein whose structure is unknown.

Also, in the 18^(th) invention of the present application, it is preferable that, when extracting a linker sequence and a non-linker loop sequence, they are divided into longer ones and shorter ones according to the length of the amino-acid sequence in each extracted region, occurrence probabilities of amino acids are obtained separately for the longer case and the shorter case, and characteristics of the sequence in each case is formulated so that the linker sequence is predicted applying a discrimination function in each case. In this way, by reflecting the trend of “how much it is like linker” in the domain linker prediction, prediction accuracy can be improved. In this case, it is preferable that the number L_(L) of amino-acid residues of longer amino-acid sequences is in a range of 8 to 50 residues both inclusive, or more preferably in a range of 10 to 50 residues both inclusive. It is preferable that the number L_(S) of amino-acid residues of longer amino-acid sequences is in a range of 4 to 12 residues both inclusive, or more preferably in a range of 4 to 9 residues both inclusive. By dividing the length of the amino-acid sequence in the loop region according to the above range and by extracting characteristics from each of them, more accurate discrimination functions can be obtained, and prediction with high accuracy is enabled.

When domain linker prediction was actually carried out with 10≦L_(L)≦50, 4≦L_(S)≦9, 52% of the predicted domain matched an actual linker sequence (specificity), and 45% of the domain linker derived from SCOP was predicted (sensitivity).

The 19^(th) invention of the present application provides a system of predicting and/or detecting a linker sequence in a multi-domain protein whose structure is unknown from characteristics of the above linker sequence on an amino-acid sequence (hereinafter referred to as “linker sequence predicting/detecting system”) comprising:

i) a means for extracting a linker sequence and a non-linker loop sequence from a database of multi-domain protein whose structure is known; and

ii) a step for obtaining, based on statistical processing of amino-acid sequence of each domain, probabilities P_(Xaa) ^(L) and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa) (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are probabilities of occurrence of the amino-acid residue X_(aa) in a linker sequence and a non-linker loop sequence, respectively) and probabilities P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of the amino-acid residues X_(aa) and Y_(aa) with m pieces (m is an integer, m=0, 1, 2) of arbitrary amino-acid residues between them (where P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are probabilities of occurrence of the amino-acid residues X_(aa) and Y_(aa) in the linker sequence and the non-linker loop sequence, respectively, with m pieces of amino acid residues between them (the order of X_(aa) and Y_(aa) does not matter)).

FIG. 20 is a flowchart explaining an operation of the linker sequence predicting/detecting system according to a preferred embodiment of the 18^(th) invention of the present application or a preferred embodiment of the 19^(th) invention of the present application.

At Step S1001, sequence information is inputted from the multi-domain protein database whose structure is known. At Step S1002, a linker sequence is extracted. At Step S1003, a non-linker loop sequence is also extracted. And at Step S1004, based on statistical processing of the amino-acid sequence of each sequence, probabilities P_(Xaa) ^(L) and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa) is obtained. Then, at Step S1005, based on statistical processing of the amino-acid sequence of each sequence, probabilities P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of the amino-acid residues X_(aa) and Y_(aa) with m pieces (m is an integer, m=0, 1, 2) of arbitrary amino-acid residues between them (the order of X_(aa) and Y_(aa) does not matter) is obtained. At Step S1006, using P_(Xaa) ^(L) and P_(XaaYaa(m)) ^(L) (P_(Xaa) ^(N) and P_(XaaYaa(m)) ^(N)), a linker sequence in the multi-domain protein whose structure is unknown is predicted and/or detected. At Step S1007, the result is outputted. The result output indicates, for example, predicted amino-acid sequences, position, length, priority, etc. of the predicted linker sequence.

FIG. 21 is a block diagram showing constitution of a linker sequence predicting/detecting system according to a preferred embodiment of the present invention. This system comprises a computer 101 provided with a CPU 102, a ROM 103, a RAM 104, an input part 105, a sending/receiving part 106, a display part 107, a hard disk drive 108 and a CD-ROM drive 109. Instead of a CD-ROM 110, a rewritable CD-R or CD-RW can be used as a recording medium. In that case, instead of the CD-ROM drive 109, a drive for CD-R or for CD-RW is provided. Instead of the CD-ROM 110, DVD, ZiP, MO, PD and their media can be used as a medium for holding information and a drive corresponding to it can be provided.

The CPU 102 controls the entire linker sequence predicting system according to the program stored in the ROM 103, the RAM 104 or the hard disk drive (HDD) 108 and executes the linker sequence predicting processing which will be described later. The ROM 103 stores programs and so on for commanding processing required for operation of the linker sequence predicting system. The RAM 104 temporarily stores data required for execution of the linker sequence predicting processing. The input part 105 includes a keyboard, mouse, etc. manipulated when inputting conditions necessary for execution of the linker sequence predicting system. The sending/receiving part 106 executes sending/receiving processing of data through a communication line based on the command of the CPU 102. The display part 107 executes processing for displaying input information, output information, etc. based on the command from the CPU 102. The hard disk drive (HDD) 108 stores the linker sequence predicting program, data sets, etc. (See FIGS. 17 through 19), reads out the stored program, data sets, etc. based on the command of the CPU 102 and stores them in the RAM 104, for example, The CD-ROM drive 109 reads out a program, data or the like from the stored program, data sets, etc. stored in the CD-ROM 110 based on the command of the CPU 102 and stores them in the hard disk drive (HDD) 108, for example,

FIG. 22 is a block diagram showing functions of a linker sequence predicting/detecting system according to a preferred embodiment of the 19^(th) invention of the present application. In a linker sequence extraction part 1021, a linker sequence portion is extracted from a multi-domain protein database whose structure is known. In a non-linker loop sequence extraction part 1022, a non-linker sequence portion is extracted from the multi-domain protein database whose structure is known. In a P_(Xaa) ^(L) (as well as P_(Xaa) ^(N)) calculation part 1023, based on statistical processing of the amino-acid sequences of the linker sequence portion and the non-linker loop sequence portion, probabilities P_(Xaa) ^(L) (P_(Xaa) ^(N)) of occurrence of an amino-acid residue X_(aa) is obtained. In a P_(XaaYaa(m)) ^(L) (as well as P_(XaaYaa(m)) ^(N)) calculation part 1024, based on statistical processing of the amino-acid sequences of the linker sequence portion and the non-linker loop sequence portion, probabilities P_(XaaYaa(m)) ^(L) (as well as P_(XaaYaa(m)) ^(N)) of occurrence of the amino-acid residues X_(aa) and Y_(aa) with m pieces (m is an integer, m=0, 1, 2) of arbitrary amino-acid residues between them (the order of X_(aa) and Y_(aa) does not matter) is obtained.

The 20^(th) invention of the present application provides a program for having a computer function as the system of the 19^(th) invention of the present application.

The 21^(st) invention of the present application provides a structural domain predicting method comprising a step for predicting as a structural domain a protein fragment generated by cutting off, at any of portions of a linker sequence in a multi-domain protein whose structure is unknown predicted by the method of the 18^(th) invention of the present application, the multi-domain protein.

FIG. 23 is a flowchart of a method of predicting a structural domain according to a preferred embodiment of the 21^(st) invention of the present application. Steps S1011 through S1016 are the same as Steps S1001 through 1006 in FIG. 2. At step S1017, a protein fragment generated by cutting off the multi-domain protein at any of portions of a linker sequence predicted at S1016 is predicted as a structural domain. At Step S1018, the result is outputted. The result output indicates, for example, predicted amino-acid sequences, position, size, etc. of the predicted structural domain.

The 22^(nd) invention of the present application is a protein producing method comprising a step for producing a protein having the same amino-acid sequence as the structural domain predicted by the method of the 21^(st) invention of the present application. For manufacture of a protein fragment, any publicly known method, that is, a chemical synthesizing method, genetic engineering method, etc. may be used.

The 23^(rd) invention of the present application is a protein analyzing method comprising a step for analyzing a protein having the same amino-acid sequence as the structural domain predicted by the method of the 21^(st) invention of the present application. As analysis of a protein fragment, in addition to the X-ray crystal structure analysis, protein structure analysis by NMR, etc., measurement of various bioactivities can be cited.

The 24^(th) invention of the present application provides a system for calculating an occurrence trend parameter of an amino-acid residue comprising:

i) a means for extracting a linker sequence and a non-linker loop sequence from a database of multi-domain protein whose structure is known;

ii) a means for obtaining, based on statistical processing of amino-acid sequence of each domain, probabilities P_(Xaa) ^(L) and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa) (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are probabilities of occurrence of the amino acid residue X_(aa) in a linker sequence and a non-linker loop sequence, respectively); and

iii) a means for obtaining an occurrence trend parameter S_(Xaa) of the amino-acid residue X_(aa) by a following equation: S _(Xaa)=log(P _(Xaa) ^(L) /P _(Xaa) ^(N)) (where, if there is no statistically significant difference between P_(Xaa) ^(L) and P_(Xaa) ^(N), it shall be S_(Xaa)=0.).

FIG. 24 is a flowchart explaining an operation of a system for calculating an occurrence trend parameter for a single amino-acid residue according to a preferred embodiment of the 24^(th) invention of the present application. Steps S1021 through S1025 are the same as Steps S1001 through 1005 in FIG. 20. At Step S1026, an occurrence trend parameter S_(Xaa) of the amino-acid residue X_(aa) is obtained by an equation of S_(Xaa)=log(P_(Xaa) ^(L)/P_(Xaa) ^(N))(however, if there is no statistically significant difference between P_(Xaa) ^(L) and P_(Xaa) ^(N), it shall be S_(Xaa)=0). At Step S1027, a calculated value of the occurrence trend parameter S_(Xaa) of the amino-acid residue X_(aa) obtained at Step S1026 is outputted. The result output indicates, for example, a value of S_(Xaa) for each amino-acid residue. Step S1027 may be omitted. If the result is to be used for the next processing (calculation processing of discrimination scores, for example), Step S1027 is omitted.

The occurrence trend parameter calculating system for an arbitrary amino-acid residue according to the 24^(th) invention of the present application is realized by a computer similar to that shown in FIG. 21, which is provided with, for example, a linker sequence extraction part 1031, a non-linker sequence extraction part 1032, a P_(Xaa) ^(L) (P_(Xaa) ^(N)) calculation part 1033, a P_(XaaYaa(m)) ^(L) (P_(XaaYaa(m)) ^(N)) calculation part 1034 and a S_(Xaa) calculation part 1035 shown in FIG. 25. The linker sequence extraction part 1031, the non-linker sequence extraction part 1032, the P_(Xaa) ^(L) (P_(Xaa) ^(N)) calculation part 1033 and the P_(XaaYaa(m)) ^(L) (P_(XaaYaa(m)) ^(N)) calculation part 1034 are the same as the linker sequence extraction part 1021, the non-linker sequence extraction part 1022, the P_(Xaa) ^(L) (P_(Xaa) ^(N)) calculation part 1023, and the P_(XaaYaa(m)) ^(L) (P_(XaaYaa(m)) ^(N)) calculation part 1024 in FIG. 22, respectively. In the S_(Xaa) calculation part 1035, the occurrence trend parameter S_(Xaa) of the amino-acid residue X_(aa) is obtained by the equation of S_(Xaa)=log(P_(Xaa) ^(L)/P_(Xaa) ^(N))(however, if there is no statistically significant difference between P_(Xaa) ^(L) and P_(Xaa) ^(N), it shall be S_(Xaa)=0).

The 25^(th) invention of the present application provides a program for having a computer function as a system of the 24^(th) invention of the present application.

The 26^(th) invention of the present application provides a system for calculating an occurrence trend parameter of an amino-acid residue pair comprising:

i) a means for extracting a linker sequence and a non-linker loop sequence from a database of multi-domain protein whose structure is known;

ii) a means for obtaining, based on statistical processing of amino acid sequence of each domain, probabilities P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of amino-acid residues X_(aa) and Y_(aa) (the order of X_(aa) and Y_(aa) does not matter) with m pieces (m is an integer, m=0, 1, 2) of arbitrary amino-acid residues between them (where P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are probabilities of occurrence of the amino-acid residues X_(aa) and Y_(aa) (the order of X_(aa) and Y_(aa) does not matter) in a linker sequence and a non-linker loop sequence, respectively, with m pieces of amino-acid residues between them) for the cases where m is 0, 1 and 2, respectively; and

iii) a means for obtaining an occurrence trend parameter S_(XaaYaa(m)) of the amino acid residue pair X_(aa) and Y_(aa) by a following equation: S _(XaaYaa(m))=log(P _(XaaYaa(m)) ^(L) /P _(XaaYaa(m)) ^(N)) (where, if there is no statistically significant difference between P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N), it shall be S_(Xaa)=0.).

FIG. 26 is a flowchart explaining an operation of an occurrence trend parameter calculating system for an amino-acid residue pair according to a preferred embodiment of the 26^(th) invention of the present application. Steps S1031 through S1035 are the same as Steps S1001 through 1005 in FIG. 20. At Step S1036, an occurrence trend parameter S_(XaaYaa(m)) of the amino-acid residue pair X_(aa) and Y_(aa) is obtained by an equation of S_(XaaYaa(m))=log (P_(XaaYaa(m)) ^(L)/P_(XaaYaa(m)) ^(N)) (however, if there is no statistically significant difference between P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N), it shall be S_(Xaa)=0). At Step S1037, a calculated value of the occurrence trend parameter S_(XaaYaa(m)) of the amino-acid residue pair X_(aa) and Y_(aa) obtained at Step S1036 is outputted. The result output indicates, for example, a value of S_(XaaYaa(m)) for each amino-acid residue pair. Step S1037 may be omitted. If the result is to be used for the next processing (calculation processing of discrimination scores, for example), Step S1037 is omitted.

The occurrence trend parameter calculating system for an arbitrary amino-acid residue pair according to the 26^(th) invention of the present application is realized by a computer similar to that shown in FIG. 21, which is provided with, for example, a linker sequence extraction part 1041, a non-linker sequence extraction part 1042, a P_(Xaa) ^(L) (P_(Xaa) ^(N)) calculation part 1043, a P_(XaaYaa(m)) ^(L) (P_(XaaYaa(m)) ^(N)) calculation part 1044 and a S_(XaaYaa(m)) calculation part 1045 shown in FIG. 27. The linker sequence extraction part 1041, the non-linker sequence extraction part 1042, the P_(Xaa) ^(L) (P_(Xaa) ^(N)) calculation part 1043 and the P_(XaaYaa(m)) ^(L) (P_(XaaYaa(m)) ^(N)) calculation part 1044 are the same as the linker sequence extraction part 1021, the non-linker sequence extraction part 1022, the P_(Xaa) ^(L) (P_(Xaa) ^(N)) calculation part 1023, and the P_(XaaYaa(m)) ^(L) (P_(XaaYaa(m)) ^(N)) calculation part 1024 in FIG. 22, respectively. In the S_(XaaYaa(m)) calculation part 1045, the occurrence trend parameter S_(XaaYaa(m)) of the amino-acid residue pair X_(aa) and Y_(aa) is obtained by the equation of S_(XaaYaa(m))=log (P_(XaaYaa(m)) ^(L)/P_(XaaYaa(m)) ^(N)) (however, if there is no statistically significant difference between P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N), it shall be S_(Xaa)=0).

The 27^(th) invention of the present application provides a program for having a computer function as a system of the 26^(th) invention of the present application.

The 28^(th) invention of the present application provides a system for obtaining a linker degree discrimination score F₁ for an amino-acid sequence with L₁ pieces (L₁ is an integer from 1 or more to 21 or less) of amino-acid residues, the system comprising:

i) a means for obtaining a linker trend score F₁s of an amino-acid residue A_(k) by an equation below: ${F_{1}s} = {\left( {\underset{k = 1}{\overset{L_{i}}{\Sigma}}S_{Ak}} \right)/L_{1}}$ (in the equation, S_(Ak)=log(P_(Ak) ^(L)/P_(Ak) ^(N))

-   where, if there is no statistically significant difference between     P_(Ak) ^(L) and P_(Ak) ^(N), it shall be S_(Ak)=0. -   Here, P_(Ak) ^(L) and P_(Ak) ^(N) are probabilities of occurrence of     the amino-acid residue A_(k) in a linker sequence and a non-linker     loop sequence, respectively.);

ii) a means for obtaining a linker trend score F₁p of an amino-acid residue pair A_(k) and A_(k+(m+1)) with m pieces (m is an integer, m=0, 1, 2) of arbitrary amino-acid residues between them by an equation below: ${F_{1}p} = {{\underset{k = 1}{\overset{L_{1}}{\Sigma}}\left( {{\underset{m = 0}{\overset{2}{\Sigma}}\left( {{S_{{AkAk} + {({m + 1})}}(m)} + {S_{{AkAk} + {({m + 1})}}(m)}} \right)}/2} \right)}/L_{1}}$ (in the equation, S_(AkAk+(m+1)(m))=log(P_(AkAk+(m+1)(m)) ^(L)/P_(AkAk+(m+1)(m)) ^(N)) and S_(AkAk−(m+1)(m))=log(P_(AkAk−(m+1)(m)) ^(L)/P_(AkAk−(m+1)(m)) ^(N))

-   where, if there is no statistically significant difference between     P_(AkAk+(m+1)(m)) ^(L) and P_(AkAk+(m+1)(m)) ^(N), or     P_(AkAk−(m+1)(m)) ^(L) and P_(AkAk−(m+1)(m)) ^(N), it shall be     S_(AkAk+(m+1)(m))=0, or S_(AkAk−(m+1)(m))=0. -   Here, P_(AkAk+(m+1)(m)) ^(L) and P_(AkAk+(m+1)(m)) ^(N) are     probabilities of occurrence of the arbitrary amino-acid residues     A_(k) and A_(k+(m+1)) in a linker sequence and a non-linker loop     sequence, respectively (the order of A_(k) and A_(k+(m+1)) does not     matter), and P_(AkAk−(m+1)(m)) ^(L) and P_(AkAk−(m+1)(m)) ^(N) are     probabilities of occurrence of the arbitrary amino-acid residues     A_(k) and A_(k−(m+1)) in the linker sequence and the non-linker loop     sequence, respectively (the order of A_(k) and A_(k−(m+1)) does not     matter)); and

iii) a means for obtaining a linker degree discrimination score F₁ by an equation below: F ₁ =F ₁ s+α ₁ F ₁ p (in the equation, 0≦α₁≦1)

A linker sequence set is a set of amino-acid sequences including at least one linker sequence, and those obtained by extracting a linker sequence portion from a multi-domain protein database whose structure is known can be cited, for example.

A non-linker loop sequence set is a set of amino-acid sequences including at least one non-linker loop sequence, and those obtained by extracting a non-linker sequence portion from a multi-domain protein database whose structure is known can be cited, for example.

FIG. 28 is a flowchart explaining an operation of a trend score calculating system for an amino-acid residue pair according to a preferred embodiment of the 28^(th) invention of the present application. At Step S1041, sequence information is inputted. The sequence information to be inputted may be any sequence information such as, for example, amino-acid sequence information from the multi-domain protein database whose structure is known, amino-acid sequence information from the multi-domain protein database whose structure is unknown, sequence information not registered in the database but newly found, etc. At Step S1042, an occurrence trend score F₁s of an arbitrary amino-acid residue is obtained by the following equation: ${F_{1}s} = {\left( {\sum\limits_{k = 1}^{L_{1}}\quad S_{Ak}} \right)/L_{1}}$ (in the equation, S_(Ak)=log(P_(Ak) ^(L)/P_(Ak) ^(N))

-   (where, P_(Ak) ^(L) is an occurrence probability of an amino-acid     residue A_(k) in a linker sequence set, while P_(Ak) ^(N) is an     occurrence probability of an amino-acid residue A_(k) in a     non-linker sequence set, but if there is no statistically     significant difference between P_(Ak) ^(L) and P_(Ak) ^(N), it shall     be S_(Ak)=0.)

At step S1043, an occurrence trend score F₁p of an amino-acid residue pair is obtained by the following equation: ${F_{1}p} = {\sum\limits_{k = 1}^{L_{1}}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{\quad{{AkAk} + {({m + 1})}}}(m)} + {S_{{AkAk} - {({m + 1})}}(m)}} \right)/2}} \right)/L_{1}}}$ (in the equation, S_(AkAk+(m+1)(m))=log(P_(AkAk+(m+1)(m)) ^(L)/P_(AkAk+(m+1)(m)) ^(N))

-   (where, P_(AkAk+(m+1)(m)) ^(L) is an occurrence probability of the     arbitrary amino-acid residues A_(k) and A_(k+(m+1)) in a linker     sequence set with m pieces (m is an integer, m=0, 1, 2) of arbitrary     amino-acid residues between them (the order of A_(k) and A_(k+(m+1))     does not matter), while P_(AkAk+(m+1)(m)) ^(N) is an occurrence     probability of the arbitrary amino-acid residues A_(k) and     A_(k+(m+1)) in a non-linker sequence set with m pieces (m is an     integer, m=0, 1, 2) of arbitrary amino-acid residues between them     (the order of A_(k) and A_(k+(m+1)) does not matter), but if there     is no statistically significant difference between P_(AkAk+(m+1)(m))     ^(L) and P_(AkAk+(m+1)(m)) ^(N), it shall be S_(AkAk+(m+1)(m))=0). -   (in the equation, S_(AkAk−(m+1)(m))=log(P_(AkAk−(m+1)(m))     ^(L)/P_(AkAk−(m+1)(m)) ^(N)) -   (where, P_(AkAk−(m+1)(m)) ^(L) is an occurrence probability of the     arbitrary amino-acid residues A_(k) and A_(k−(m+1)) in a linker     sequence set with m pieces (m is an integer, m=0, 1, 2) of arbitrary     amino-acid residues between them (the order of A_(k) and A_(k−(m+1))     does not matter), while P_(AkAk−(m+1)(m)) ^(N) is an occurrence     probability of the arbitrary amino-acid residues A_(k) and     A_(k−(m+1)) in a non-linker sequence set with m pieces (m is an     integer, m=0, 1, 2) of arbitrary amino-acid residues between them     (the order of A_(k) and A_(k−(m+1)) does not matter), but if there     is no statistically significant difference between P_(AkAk−(m+1)(m))     ^(L) and P_(AkAk−(m+1)(m)) ^(N), it shall be S_(AkAk−(m+1)(m))=0).

At Step S1044, the linker degree discrimination score F₁ is obtained by an equation below: F ₁ =F ₁ s+α ₁ F ₁ p (in the equation, 0≦α₁≦1)

At Step S1045, the linker degree discrimination score F₁ obtained at Step S1044 is outputted. The result output indicates, for example, an amino-acid residue, a value of F₁ of each amino-acid sequence, etc. Step S1045 may be omitted. If the result is to be used for the next processing (construction processing of domain linker database, for example), Step S1045 is omitted.

The system for obtaining the linker degree discrimination score F₁s of the 28^(th) invention of the present invention is realized by a computer similar to that shown in FIG. 21, which is provided with, for example, an F₁s calculation part 1051, an F₁p calculation part 1052, and an F₁ calculation part 1053. In the F₁s calculation part 1051, the occurrence trend score F₁s of an amino-acid residue is obtained by the above equation. In the F₁p calculation part 1052, the occurrence trend score F₁p of an amino-acid residue pair is obtained by the above equation. In the F₁ calculation part 1053, the linker degree discrimination score F₁ is obtained by the above equation

The 29^(th) invention of the present application provides a program for having a computer function as a system of the 28^(th) invention of the present application.

The 30^(th) invention of the present application provides a method of obtaining a linker degree discrimination score F₁₁(i) for an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues by taking a window of w pieces of amino-acid residues before and after the amino-acid residue at the position i (i is an integer from 1 or more to L₂ or less) comprising:

i) a step for obtaining a linker trend score F₁₁s(i) of an amino-acid residue A_(k) by an equation below: ${F_{11}{s(i)}} = {\left( {\sum\limits_{k = {i - w}}^{i + w}\quad S_{\quad{Ak}}} \right)/W}$ (in the equation, W is a window width, and W=2w+1, S_(Ak)=log(P_(Ak) ^(L)/P_(Ak) ^(N))

-   where, if there is no statistically significant difference between     P_(Ak) ^(L) and P_(Ak) ^(N), it shall be S_(Ak)=0. -   Here, P_(Ak) ^(L) and P_(Ak) ^(N) are probabilities of occurrence of     the amino-acid residue A_(k) in a linker sequence and a non-linker     loop sequence, respectively.);

ii) a step for obtaining the linker trend score F₁₁p(i) of an amino-acid residue pair A_(i) and A_(i+(m+1)) with m pieces (m is an integer, m=0, 1, 2) of arbitrary amino-acid residues between them by an equation below: ${F_{11}{p(i)}} = {\sum\limits_{k = {i - w}}^{i + w}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{\quad{{AiAi} + {({m + 1})}}}(m)} + {S_{{AiAi} - {({m + 1})}}(m)}} \right)/2}} \right)/W}}$ (in the equation, S_(AiAi+(m+1)(m))=log(P_(AiAi+(m+1)(m)) ^(L)/P_(AiAi+(m+)(m)) ^(N)), and S_(AiAi−(m+1)(m))=log(P_(AiAi−(m+)(m)) ^(L)/P_(AiAi−(m+1)(m)) ^(N))

-   where, if there is no statistically significant difference between     P_(AiAi+(m+1)(m)) ^(L) and P_(AiAi+(m+1)(m)) ^(N), or     P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N), it shall be     S_(AiAi+(m+1)(m))=0, or S_(AiAi−(m+1)(m))=0. -   Here, P_(AiAi+(m+1)(m)) ^(L) and P_(AiAi+(m+1)(m)) ^(N) are     probabilities of occurrence of the arbitrary amino-acid residue pair     A_(i) and A_(i+(m+1)) in a linker sequence and a non-linker loop     sequence, respectively (the order of A_(i) and A_(i+(m+1)) does not     matter), and P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N) are     probabilities of occurrence of the arbitrary amino-acid residues     A_(i) and A_(i−(m+1)) in the linker sequence and the non-linker loop     sequence, respectively (the order of A_(i) and A_(i−(m+1)) does not     matter)); and

iii) a step for obtaining the linker degree discrimination score F₁₁(i) of the amino-acid residue A_(i) at the position i by an equation below: F ₁₁(i)=F ₁₁ s(i)+α₁₁ F ₁₁ p(i) (in the equation, 0≦α₁₁≦1)

In FIG. 53, how to take a window is shown.

The window width W is preferably 5 through 21, more preferably 9 through 13.

The 31^(st) invention of the present invention provides a system for obtaining a linker degree discrimination score F₁₁(i) for an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues by taking a window of w pieces of amino-acid residues before and after the amino-acid residue at the position i (i is an integer from 1 or more to L₂ or less) comprising:

i) a means for obtaining a linker trend score F₁₁s(i) of an amino-acid residue A_(k) by an equation below: ${F_{11}{s(i)}} = {\left( {\sum\limits_{k = {i - w}}^{i + w}\quad S_{\quad{Ak}}} \right)/W}$ (in the equation, W is a window width, and W=2w+1, S_(Ak)=log(P_(Ak) ^(L)/P_(Ak) ^(N))

-   where, if there is no statistically significant difference between     P_(Ak) ^(L) and P_(Ak) ^(N), it shall be S_(Ak)=0. -   Here, P_(Ak) ^(L) and P_(Ak) ^(N) are probabilities of occurrence of     the amino-acid residue A_(k) in a linker sequence and a non-linker     loop sequence, respectively.);

ii) a means for obtaining the linker trend score F₁₁p(i) of an amino-acid residue pair A_(i) and A_(i+(m+1)) with m pieces (m is an integer, m=0, 1, 2) of arbitrary amino-acid residues between them by an equation below: ${F_{11}{p(i)}} = {\sum\limits_{k = {i - w}}^{i + w}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{\quad{{AiAi} + {({m + 1})}}}(m)} + {S_{{AiAi} - {({m + 1})}}(m)}} \right)/2}} \right)/W}}$ (in the equation, S_(AiAi+(m+1)(m))=log(P_(AiAi+(m+1)(m)) ^(L)/P_(AiAi+(m+1)(m)) ^(N)), and S_(AiAi−(m+1)(m))=log(P_(AiAi−(m+1)(m)) ^(L)/P_(AiAi−(m+1)(m)) ^(N))

-   where, if there is no statistically significant difference between     P_(AiAi+(m+1)(m)) ^(L) and P_(AiAi+(m+1)(m)) ^(N), or     P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N), it shall be     S_(AiAi+(m+1)(m))=0, or S_(AiAi−(m+1)(m))=0. -   Here, P_(AiAi+(m+1)(m)) ^(L) and P_(AiAi+(m+1)(m)) ^(N) are     probabilities of occurrence of the arbitrary amino-acid residue pair     A_(i) and A_(i+(m+1)) in a linker sequence and a non-linker loop     sequence, respectively (the order of A_(i) and A_(i+(m+1)) does not     matter), and P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N) are     probabilities of occurrence of the arbitrary amino-acid residue pair     A_(i) and A_(i−(m+1)) in the linker sequence and the non-linker loop     sequence, respectively (the order of A_(i) and A_(i−(m+1)) does not     matter)); and

iii) a means for obtaining the linker degree discrimination score F₁₁(i) of the amino-acid residue Ai at the position i by an equation below: F ₁₁(i)=F ₁₁ s(i)+α₁₁ F ₁₁ p(i) (in the equation, 0≦α₁₁≦1)

FIG. 30 is a flowchart explaining an operation of a system for obtaining a linker degree discrimination score F₁₁(i) according to a preferred embodiment of the 30^(th) invention of the present application or a system for obtaining a linker degree discrimination score F₁₁(i) according to a preferred embodiment of the 31^(st) invention of the present application.

At Step S1061, sequence information is inputted. The sequence information to be inputted may be any sequence information such as, for example, sequence information from the multi-domain protein database whose structure is known, sequence information from the multi-domain protein database whose structure is unknown, sequence information not registered in the database but newly found, etc.

At Step S1062, an occurrence trend score F₁₁s(i) of an arbitrary amino-acid residue is obtained by the following equation: ${F_{11}{s(i)}} = {\left( {\sum\limits_{k = {i - w}}^{i + w}\quad S_{\quad{Ak}}} \right)/W}$ (in the equation, W is a window width, and W=2w+1, S_(Ak)=log(P_(Ak) ^(L)/P_(Ak) ^(N))

-   (where, P_(Ak) ^(L) is an occurrence probability of an amino-acid     residue A_(k) in a linker sequence set, while P_(Ak) ^(N) is an     occurrence probability of an amino-acid residue A_(k) in a     non-linker sequence set, but if there is no statistically     significant difference between P_(Ak) ^(L) and P_(Ak) ^(N), it shall     be S_(Ak)=0.)

At step S1063, an occurrence trend score F₁₁p(i) of an amino-acid residue pair is obtained by the following equation: ${F_{11}{p(i)}} = {\sum\limits_{k = {i - w}}^{i + w}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{\quad{{AiAi} + {({m + 1})}}}(m)} + {S_{{AiAi} - {({m + 1})}}(m)}} \right)/2}} \right)/W}}$ (in the equation, S_(AiAi+(m+1)(m))=log(P_(AiAi+(m+1)(m)) ^(L)/P_(AiAi+(m+1)(m)) ^(N)))

-   (where, P_(AiAi+(m+1)(m)) ^(L) is an occurrence probability of the     arbitrary amino-acid residues A_(i) and A_(i+(m+1)) in a linker     sequence set with m pieces (m is an integer, m=0, 1, 2) of arbitrary     amino-acid residues between them (the order of A_(i) and A_(i+(m+1))     does not matter), while P_(AiAi+(m+1)(m)) ^(N) is an occurrence     probability of the arbitrary amino-acid residues A_(i) and     A_(i+(m+1)) in a non-linker sequence set with m pieces (m is an     integer, m=0, 1, 2) of arbitrary amino-acid residues between them     (the order of A_(i) and A_(i+(m+1)) does not matter), but if there     is no statistically significant difference between P_(AiAi+(m+1)(m))     ^(L) and P_(AiAi+(m+1)(m)) ^(N), it shall be S_(AiAi+(m+1)(m))=0).     S_(AiAi−(m+1)(m))=log(P_(AiAi−(m+1)(m)) ^(L)/P_(AiAi−(m+1)(m))     ^(N))) -   (where, P_(AiAi−(m+1)(m)) ^(L) is an occurrence probability of the     arbitrary amino-acid residues A_(i) and A_(i−(m+1)) in a linker     sequence set with m pieces (m is an integer, m=0, 1, 2) of arbitrary     amino-acid residues between them (the order of A_(i) and A_(i−(m+1))     does not matter), while P_(AiAi+(m+1)(m)) ^(N) is an occurrence     probability of the arbitrary amino-acid residues A_(i) and     A_(i−(m+1)) in a non-linker sequence set with m pieces (m is an     integer, m=0, 1, 2) of arbitrary amino-acid residues between them     (the order of A_(i) and A_(i−(m+1)) does not matter), but if there     is no statistically significant difference between P_(AiAi−(m+1)(m))     ^(L) and P_(AiAi−(m+1)(m)) ^(N), it shall be S_(AiAi−(m+1)(m))=0).

At Step S1064, the linker degree discrimination score F₁₁(i) is obtained by an equation below: F ₁₁(i)=F ₁₁ s(i)+α₁₁ F ₁₁ p(i) (in the equation, 0≦α₁₁≦1)

Steps S1062 to S1064 are executed for all the amino-acid residues Ai at the position i existing in the range of 1 or more to L₂ or less.

At Step S1065, the linker degree discrimination score F₁₁(i) obtained at Step S1064 is outputted. The result output indicates, for example, an amino-acid sequence, the position i and a value of corresponding F₁₁(i), etc. Step S1065 may be omitted. If the result is to be used for the next processing (prediction processing of domain linker, for example), Step S1065 is omitted.

The system for obtaining the linker degree discrimination score F₁₁(i) of the 31^(st) invention of the present invention is realized by a computer similar to that shown in FIG. 21, which is provided with, for example, an F₁₁s(i) calculation part 1071, an F₁₁p(i) calculation part 1072, and an F₁₁(i) calculation part 1073. In the F₁₁s(i) calculation part 1071, the F₁₁p(i) calculation part 1072, and the F₁₁(i) calculation part 1073, F₁₁s(i), F₁₁p(i) and the linker degree discrimination score F₁₁(i) is obtained by the above equations, respectively.

The 32^(nd) invention of the present application provides a program for having a computer function as a system of the 31^(st) invention of the present application.

The 33^(rd) invention of the present application provides a method of obtaining a linker degree discrimination score F₁₂(i) of an amino-acid residue Ai at a position i in an amino-acid sequence seq.0 with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues for which existence of n pieces (n is an integer of 1 or more) of homologous sequences seq.1˜seq.n is known by taking a window with w pieces of the amino-acid residues before and after the amino-acid residue at the position i (i is an integer from 1 or more to 22 or less) comprising:

i) a step for identifying an amino-acid residue A_(i) ^(k) in a seq.k (k is an integer from 1 or more and n or less) corresponding to an amino-acid residue Ai⁰ at a position i in the seq.0 by aligning seq.0 and seq.1˜seq.n;

ii) a step for obtaining parameters S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) of the amino-acid residue Ai at the position i by an equation below: $S_{Ai}^{\prime} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{\quad{Ai}}k}} \right)/\left( {n - n_{{gap}\quad 1}} \right)}$ ${S_{{AiAi} + {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{\quad{Ai}}k_{{Ai} + {({m + 1})}}{k(m)}}} \right)/\left( {n - n_{{gap}\quad 2}} \right)}$ ${S_{{AiAi} - {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{\quad{Ai}}k_{{Ai} - {({m + 1})}}{k(m)}}} \right)/\left( {n - n_{{gap}\quad 3}} \right)}$ (in the equation, n_(gap1) is the number of gaps occurring in A_(i) ^(k), S_(Ai)k=log(P_(Ai)k^(L)/P_(Ai)k^(N))

-   where, if there is no statistically significant difference between     P_(Ai)k^(L) and P_(Ai)k^(N), it shall be S_(Ai)k=0. -   Here, P_(Ai)k^(L) and P_(Ai)k^(N) are probabilities of occurrence of     the amino-acid residue A_(i) ^(k) in a linker sequence and a     non-linker loop sequence, respectively.

Also, in the equation, n_(gap2) is the number of gaps occurring in A_(i) ^(k) or A_(i+(m+1)) ^(k), S _(Ai) k _(Ai+(m+1)) k(m)=log(P _(Ai) k _(Ai+(m+1)) k _((m)) ^(L) /P _(Ai) k _(Ai+(m+1)) k _((m)) ^(N)) where, if there is no statistically significant difference between P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m)) ^(N), it shall be S_(Ai)k_(Ai+(m+1))k_((m))=0.

-   Here, P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m))     ^(N) are probabilities of occurrence of the arbitrary amino-acid     residues A_(i) ^(k) and A_(i+(m+1)k) in a linker sequence and a     non-linker loop sequence, respectively (the order of A_(i) ^(k) and     A_(i+(m+1)) ^(k) does not matter) with m pieces (m is an integer,     m=0, 1, 2) of arbitrary amino-acid residues between them.

Moreover, in the equation, n_(gap3) is the number of gaps occurring in A_(i) ^(k) or A_(i−(m+1)) ^(k), S _(Ai) k _(Ai−(m+1)) k _((m))=log(P _(Ai) k _(Ai−(m+1)) k _((m)) ^(L) /P _(Ai) k _(Ai−(m+1)) k _((m)) ^(N))

-   where, if there is no statistically significant difference between     P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m)) ^(N),     it shall be S_(Ai)k_(Ai−(m+1))k_((m))=0. -   Here, P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m))     ^(N) are probabilities of occurrence of the amino-acid residues     A_(i) ^(k) and A_(i−(m+1)) ^(k) in a linker sequence and a     non-linker loop sequence, respectively (the order of A_(i) ^(k) and     A_(i−(m+1)) ^(k) does not matter) with m pieces (m is an integer,     m=0, 1, 2) of arbitrary amino-acid residues between them.);

iii) a step for obtaining a linker trend score F₁₂s(i) of an amino-acid residue by an equation below: ${F_{12}{s(i)}} = {\left( {\sum\limits_{k = {i - w}}^{i + w}\quad S_{\quad{Ak}}^{\prime}} \right)/W}$

iv) a step for obtaining a linker trend score F₁₂p(i) of an arbitrary amino-acid residue pair by an equation below: and ${F_{12}{p(i)}} = {\sum\limits_{k = {i - w}}^{i + w}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{{AiAi} + {({m + 1})}}^{\prime}(m)} + {S_{{AiAi} - {({m + 1})}}^{\prime}(m)}} \right)/2}} \right)/W}}$

v) a step for obtaining the linker degree discrimination score F₁₂(i) of the amino-acid residue Ai at the position i by an equation below: F ₁₂(i)=F ₁₂ s(i)+α₁₂ F ₁₂ p(i)

-   (in the equation, 0≦α₁₂≦1)

In FIG. 54, sequences of aligned seq.0 and seq.1 through seq.n and how to take a window are shown.

The 34^(th) invention of the present application is a system for obtaining a linker degree discrimination score F₁₂(i) of an amino-acid residue Ai at a position i in an amino-acid sequence seq.0 with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues for which existence of n pieces (n is an integer of 1 or more) of homologous sequences seq.1˜seq.n is known, by taking a window with w pieces of amino-acid residues before and after the amino-acid residue at the position i (i is an integer from 1 or more to 22 or less) comprising:

i) a means for identifying an amino-acid residue A_(i) ^(k) in a seq.k (k is an integer from 1 or more and n or less) corresponding to an amino-acid residue Ai⁰ at the position i in the seq.0 by aligning seq.0 and seq.1˜seq.n;

ii) a means for obtaining parameters of the amino-acid residue Ai at the position i, S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) by an equation below: $S_{Ai}^{\prime} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k}} \right)/\left( {n - n_{{gap}\quad 1}} \right)}$ ${S_{{AiAi} + {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k_{{Ai} + {({m + 1})}}{k(m)}}} \right)/\left( {n - n_{{gap}\quad 2}} \right)}$ ${S_{{AiAi} - {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k_{{Ai} - {({m + 1})}}{k(m)}}} \right)/\left( {n - n_{{gap}\quad 3}} \right)}$ (in the equation, n_(gap1) is the number of gaps occurring in A_(i) ^(k), S_(Ai)k=log(P_(Ai)k^(L)/P_(Ai)k^(N))

-   where, if there is no statistically significant difference between     P_(Ai)k^(L) and P_(Ai)k^(N), it shall be S_(Ai)k=0. -   Here, P_(Ai)k^(L) and P_(Ai)k^(N) are probabilities of occurrence of     the amino-acid residue A_(i) ^(k) in a linker sequence and a     non-linker loop sequence, respectively.

Also, in the equation, n_(gap2) is the number of gaps occurring in A_(i) ^(k) or A_(i+(m+1)) ^(k), S _(Ai) k _(Ai+(m+1)) k _((m))=log(P _(Ai) k _(Ai+(m+1)) k _((m)) ^(L) /P _(Ai) k _(Ai+(m+1)) k _((m)) ^(N)) where, if there is no statistically significant difference between P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m)) ^(N), it shall be S_(Ai)k_(Ai+(m+1))k_((m))=0.

-   Here, P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m))     ^(N) are probabilities of occurrence of the amino-acid residues     A_(i) ^(k) and A_(i+(m+1)) ^(k) in the linker sequence and the     non-linker loop sequence, respectively (the order of A_(i) ^(k) and     A_(i+(m+1)) ^(k) does not matter) with m pieces (m is an integer,     m=0, 1, 2) of arbitrary amino-acid residues between them.

Moreover, in the equation, n_(gap3) is the number of gaps occurring in A_(i) ^(k) or A_(i−(m+1)) ^(k), S _(Ai) k _(Ai−(m+1)) k _((m))=log(P _(Ai) k _(Ai−(m+1)) k _((m)) ^(L) /P _(Ai) k _(Ai−(m+1)) k _((m)) ^(N)) where, if there is no statistically significant difference between P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m)) ^(N), it shall be S_(Ai)k_(Ai−(m+1))k_((m))=0.

-   Here, P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m))     ^(N) are probabilities of occurrence of the amino-acid residues     A_(i) ^(k) and A_(i−(m+1)) ^(k) in the linker sequence and the     non-linker loop sequence, respectively (the order of A_(i) ^(k) and     A_(i−(m+1)) ^(k) does not matter) with m pieces (m is an integer,     m=0, 1, 2) of arbitrary amino acid residues between them.);

iii) a means for obtaining a linker trend score F₁₂s(i) of an amino-acid residue by an equation below; ${F_{12}{s(i)}} = {\left( {\sum\limits_{k = {i - w}}^{i + w}\quad S_{Ak}^{\prime}} \right)/W}$

iv) a means for obtaining a linker trend score F₁₂p(i) of an arbitrary amino-acid residue pair by an equation below; and ${F_{12}{p(i)}} = {\sum\limits_{k = {i - w}}^{i + w}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{{AiAi} + {({m + 1})}}^{\prime}(m)} + {S_{{AiAi} - {({m + 1})}}^{\prime}(m)}} \right)/2}} \right)/W}}$

v) a means for obtaining the linker degree discrimination score F₁₂(i) of the amino-acid residue Ai at the position i by an equation below. F ₁₂(i)=F ₁₂ s(i)+α₁₂ F ₁₂ p(i) (in the equation, 0≦α₁₂≦1)

FIG. 32 is a flowchart explaining an operation of a method of obtaining a linker degree discrimination score F₁₂(i) according to a preferred embodiment of the 33^(rd) invention of the present application or a system for obtaining a linker degree discrimination score F₁₂(i) of the 34^(th) invention of the present application.

At Step S1071, sequence information is inputted. The sequence information to be inputted may be any sequence information such as, for example, sequence information from the multi-domain protein database whose structure is known, sequence information from the multi-domain protein database whose structure is unknown, sequence information not registered in the database but newly found, etc.

At Step S1072, the amino-acid residue A_(i) ^(k) in the seq.k (k is an integer from 1 or more and n or less) corresponding to the amino-acid residue Ai⁰ at the position i in the seq.0 is identified by aligning seq.0 and seq.1˜seq.n,

-   k is an integer

At Step S1073, the parameters S′_(Ai); S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) of the amino-acid residue Ai at the position i are obtained by an equation below: $S_{Ai}^{\prime} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k}} \right)/\left( {n - n_{{gap}\quad 1}} \right)}$ ${S_{{AiAi} + {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k_{{Ai} + {({m + 1})}}{k(m)}}} \right)/\left( {n - n_{{gap}\quad 2}} \right)}$ ${S_{{AiAi} - {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k_{{Ai} - {({m + 1})}}{k(m)}}} \right)/\left( {n - n_{{gap}\quad 3}} \right)}$ (in the equation, n_(gap1) is the number of gaps occurring in A_(i) ^(k), S_(Ai)k=log(P_(Ai)k^(L)/P_(Ai)k^(N))

-   (where, P_(Ai)k^(L)is an occurrence probability of the amino-acid     residue A_(i) ^(k) in a linker sequence and P_(Ai)k^(N) is an     occurrence probability of the amino-acid residue A_(i) ^(k) in a     non-linker loop sequence, but if there is no statistically     significant difference between P_(Ai)k^(L) and P_(Ai)k^(N), it shall     be S_(Ai) ^(k)=0.) -   (in the equation, n_(gap2) is the number of gaps occurring in A_(i)     ^(k) or A_(i+(m+1)) ^(k),     S_(Ai)k_(Ai+(m+1))k_((m))=log(P_(Ai)k_(Ai+(m+1))k_((m))     ^(L)/P_(Ai)k_(Ai+(m+1))k_((m)) ^(N)) -   (in the equation, P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) is an occurrence     probability of the amino-acid residues A_(i) ^(k) and A_(i+(m+1))     ^(k) in the linker sequence set (the order of A_(i) ^(k) and     A_(i+(m+1)) ^(k) does not matter) with m pieces (m is an integer,     m=0, 1, 2) of arbitrary amino-acid residues between them, and     P_(Ai)k_(Ai+(m+1))k_((m)) ^(N) is an occurrence probability of the     amino-acid residues A_(i) ^(k) and A_(i+(m+1)) ^(k) in the     non-linker sequence set (the order of A_(i) ^(k) and A_(i+(m+1))     ^(k) does not matter) with m pieces (m is an integer, m=0, 1, 2) of     arbitrary amino-acid residues between them, but if there is no     statistically significant difference between     P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m)) ^(N),     it shall be S_(Ai)k_(Ai+(m+1))k_((m))=0. -   (in the equation, n_(gap3) is the number of gaps occurring in A_(i)     ^(k) or A_(i−(m+1)) ^(k),     S_(Ai)k_(Ai−(m+1))k_((m))=log(P_(Ai)k_(Ai−(m+1))k_((m))     ^(L)/P_(Ai)k_(Ai−(m+1))k_((m)) ^(N)) -   (in the equation, P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) is an occurrence     probability of the amino-acid residues A_(i) ^(k) and A_(i−(m+1))     ^(k) in the linker sequence set (the order of A_(i) ^(k) and     A_(i−(m+1)) ^(k) does not matter) with m pieces (m is an integer,     m=0, 1, 2) of arbitrary amino acid residues between them, and     P_(Ai)k_(Ai−(m+1))k_((m)) ^(N) is an occurrence probability of the     amino-acid residues A_(i) ^(k) and A_(i−(m+1)) ^(k) in the     non-linker loop sequence set (the order of A_(i) ^(k) and     A_(i−(m+1)) ^(k) does not matter) with m pieces (m is an integer,     m=0, 1, 2) of arbitrary amino acid residues between them, but if     there is no statistically significant difference between     P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m)) ^(N),     it shall be S_(Ai)k_(Ai−(m+1))k_((m))=0.);

At Step S1074, the single amino-acid residue trend score F₁₂s(i) is obtained by an equation below; ${F_{12}{s(i)}} = {\left( {\sum\limits_{k = {i - w}}^{i + w}\quad S_{Ak}^{\prime}} \right)/W}$

At Step S1075, the occurrence trend score F₁₂p(i) of an arbitrary amino-acid residue pair by an equation below: ${F_{12}{p(i)}} = {\sum\limits_{k = {i - w}}^{i + w}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{{AiAi} + {({m + 1})}}^{\prime}(m)} + {S_{{AiAi} - {({m + 1})}}^{\prime}(m)}} \right)/2}} \right)/W}}$

At Step S1076, the linker degree discrimination score F₁₂(i) of the amino-acid residue Ai at the position i by an equation below. F ₁₂(i)=F ₁₂ s(i)+α₁₂ F ₁₂ p(i) (in the equation, 0≦α₁₂≦1)

Steps S1072 to S1076 are executed for all the amino-acid residues Ai at the position i existing in the range of 1 or more to L₂ or less.

At Step S1077, the linker degree discrimination score F₁₂(i) obtained at Step S1076 is outputted. The result output indicates, for example, an amino-acid sequence, the position i and a value of corresponding F₁₂(i), etc. Step S1077 may be omitted. If the result is to be used for the next processing (prediction processing of domain linker, for example), Step S1077 is omitted.

The system for obtaining the linker degree discrimination score F₁₂(i) of the 34^(th) invention of the present invention is realized by a computer similar to that shown in FIG. 21, which is provided with, for example, an A_(i) ^(k) identification part 1081, an S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) calculation part 1082, an F₁₂s(i) calculation part 1083, and an F₁₂p(i) calculation part 1084, and an F₁₂(i) calculation part 1085. In the A_(i) ^(k) identification part 1081, the amino-acid residue A_(i) ^(k) in the seq.k (k is an integer from 1 or more and n or less) corresponding to the amino-acid residue Ai⁰ at the position i in the seq.0 is identified by aligning seq.0 and seq.1˜seq.n. In the S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) calculation part 1082, the parameters S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) of the amino-acid residue Ai at the position i are obtained by an above equation. In the F₁₂s(i) calculation part 1083, the F₁₂p(i) calculation part 1084, and the F₁₂(i) calculation part 1085, respectively, F₁₂s(i), F₁₂p(i) and F₁₂(i) are obtained by the above equations, respectively.

The 35^(th) invention of the present application provides a program having a computer function as a system of the 34^(th) invention of the present application.

The 36^(th) invention of the present application provides a method of predicting a domain linker portion comprising:

i) a step for obtaining a linker degree discrimination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues according to the method of the 30^(th) or the 33^(rd) invention of the present application (however, a linker degree discrimination score does not have to be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence);

ii) a step for obtaining a region predicted to take a loop structure for the amino-acid sequence by executing secondary-structure prediction;

iii) a step for obtaining a region which is predicted to take the loop structure in the secondary-structure prediction and whose linker degree discrimination score is larger than 0; and

iv) a step for predicting for each region in iii) a position where the linker degree discrimination score becomes the maximum value as a position where the domain linker exists.

FIG. 54 shows an outline of the method of predicting a domain linker portion. In Fig., a query sequence is an amino-acid sequence of seq.0, and F(i) is a linker degree discrimination score (the above F₁, F₂(i), F₁₁(i) and F₁₂(i), for example).

The secondary structure prediction can be executed using a program such as DSC (by R. D. King, M. J. E. Sternberg (1996)) or the like.

The 37^(th) invention of the present application provides a system for predicting a domain linker portion comprising:

i) a means for obtaining a linker degree discrimination score of an amino acid residue Ai at a position i in an amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues according to the method of the 30^(th) or the 33^(rd) invention of the present application (however, a linker degree discrimination score does not have to be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence);

ii) a means for obtaining a region predicted to take a loop structure for the amino-acid sequence by executing secondary-structure prediction;

iii) a means for obtaining a region which is predicted to take the loop structure in the secondary-structure prediction and whose linker degree discrimination score is larger than 0; and

iv) a means for predicting for each region in iii) a position where the linker degree discrimination score becomes the maximum value as a position where the domain linker exists.

FIG. 34 is a flowchart explaining an operation of a method of predicting a domain linker portion according to a preferred embodiment of the 36^(th) invention of the present application or a predicting system for a domain linker portion according to a preferred embodiment of the 37^(th) invention of the present application.

Steps S1081 through S1084 are the same as Steps S1061 through S1064 in FIG. 30. At Step S1085, a region predicted to take a loop structure is obtained for the amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues by executing secondary-structure prediction. At Step S1086, a region which is predicted to take the loop structure in the secondary-structure prediction and whose linker degree discrimination score is larger than 0 is obtained. At Step S1087, a position where the linker degree discrimination score becomes the maximum value is predicted as a position where the domain linker exists for each region obtained at Step S1086. At Step S1077, the result is outputted. The result output indicates, for example, the predicted sequences, the position, length, priority, etc. of the predicted linker sequence.

A preferred embodiment of the predicting system of a domain linker portion of the 37^(th) invention of the present application shown in FIG. 34 is realized by a computer similar to that shown in FIG. 21, which is provided with, for example, an F₁₁s(i) calculation part 1091, an F₁₁p(i) calculation part 1092, and an F₁₁(i) calculation part 1093, a secondary structure prediction part 1094, a region search part 1095 and a domain linker existing position prediction part 1096 shown in FIG. 35. The F₁₁s(i) calculation part 1091, the F₁₁p(i) calculation part 1092, and the F₁₁(i) calculation part 1093 are the same as an F₁₁s(i) calculation part 1071, an F₁₁p(i) calculation part 1072, and an F₁₁(i) calculation part 1073 in FIG. 31, respectively. In the secondary structure prediction part 1094, secondary structure prediction is executed for the amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues, and a region predicted to take a loop structure is obtained. In the region search part 1095, a region which is predicted to take the loop structure in the secondary-structure prediction and whose linker degree discrimination score is larger than 0 is obtained. In the domain linker existing position prediction part 1096, a position where the linker degree discrimination score becomes the maximum value is predicted as a position where the domain linker exists for each region obtained in the region search part 1095.

FIG. 36 is a flowchart explaining an operation of a method of predicting a domain linker portion according to a preferred embodiment of the 36^(th) invention of the present application or a predicting system for a domain linker portion according to a preferred embodiment of the 37^(th) invention of the present application.

Steps S1091 through S1096 are the same as Steps S1071 through S1076 in FIG. 32. Steps S1097 through S1100 are the same as Steps S1085 through S1088 in FIG. 34.

Another preferred embodiment of the predicting system of a domain linker portion of the 37^(th) invention of the present application shown in FIG. 36 is realized by a computer similar to that shown in FIG. 21, which is provided with, for example, an A_(i) ^(k) identification part 1101, an S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) calculation part 1102, an F₁₂s(i) calculation part 1103, and an F₁₂p(i) calculation part 1104, an F₁₂(i) calculation part 1105, a secondary structure prediction part 1106, a region search part 1107, and a domain linker existing position prediction part 1108 shown in FIG. 37. The A_(i) ^(k) identification part 1101, the S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) calculation part 1102, the F₁₂s(i) calculation part 1103, and the F₁₂p(i) calculation part 1104, the F₁₂(i) calculation part 1105 are the same as the A_(i) ^(k) identification part 1081, the S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) calculation part 1082, the F₁₂s(i) calculation part 1083, and the F₁₂p(i) calculation part 1084, the F₁₂(i) calculation part 1085 in FIG. 33, respectively. The secondary structure prediction part 1106, the region search part 1107, and the domain linker existing position prediction part 1108 are the same as the secondary structure prediction part 1094, the region search part 1095, and the domain linker existing position prediction part 1096 in FIG. 35, respectively.

The 38^(th) invention of the present application provides a program for having a computer function as a system of the 37^(th) invention of the present application.

The 39^(th) invention of the present application provides a method of constructing an amino-acid sequence database comprising:

i) a step for obtaining a linker degree discrimination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues according to the method of the 30^(th) or the 33^(rd) invention of the present application (however, a linker degree discrimination score does not have to be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence);

ii) a step for obtaining a region predicted to take a loop structure for the amino-acid sequence by executing secondary-structure prediction;

iii) a step for obtaining a region which is predicted to take the loop structure in the secondary-structure prediction and whose linker degree discrimination score is larger than 0;

iv) a step for selecting a region from those obtained in iii) whose maximum value of the linker degree discrimination score is larger than a lower limit value; and

v) a step for recording an amino-acid sequence of a region selected in iv) in a recording medium.

The lower limit value in the step iv) is preferably any value not less than 0, and preferably any value from 0.0 to 1.0.

In the step v), as a recording medium for recording the amino-acid sequence of a region selected in iv) may be a magnetic tape, cassette tape, flexible disk, hard disk, CD-ROM, MO/MD/DVD, etc. or semiconductor memory.

The 40^(th) invention of the present application provides a domain linker peptide made of an amino-acid sequence which is the same as the amino-acid sequence in a region whose maximum value of a linker degree discrimination score is larger than a lower limit value, obtained from a method comprising:

i) a step for obtaining a linker degree discrimination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino acid residues according to a method of the 30^(th) or the 33^(rd) invention of the present application (however, a linker degree discrimination score does not have to be obtained for 0 to 50 residues at the N and C terminals of the amino acid sequence);

ii) a step for obtaining a region predicted to take a loop structure for the amino-acid sequence by executing secondary-structure prediction;

iii) a step for obtaining a region which is predicted to take the loop structure in the secondary-structure prediction and whose linker trend discrimination score is larger than 0; and

iv) a step for selecting a region from those obtained in iii) whose maximum value of the linker degree discrimination score is larger than the lower limit value.

The 41^(st) invention of the present application provides a method of predicting a structural domain comprising a step for predicting, concerning an amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues, a sequence fragment generated by cutting off the amino-acid sequence at any portion of a region including a domain linker portion or a domain-linker existing position predicted by the method of the 36^(th) invention of the present application as a structural domain. In this 41^(st) invention of the present application, if n pieces of domain linker portions are predicted, t piece(s) (t is an integer from 1 or more to n or less) among them is (are) selected, all the patterns for cutting an amino acid sequence at that position are considered, and all the obtained sequence fragments may be predicted as structural domains.

The 42^(nd) invention of the present application provides a system for predicting a structural domain (hereinafter referred to as “structural domain predicting system”) comprising a means for predicting, concerning an amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues, a sequence fragment generated by cutting off the amino-acid sequence at any portion of a region including a domain linker portion or a domain-linker existing position predicted by the method of the 36^(th) invention of the present application as a structural domain.

The structural domain may be those existing in a multi-domain protein.

FIG. 38 is a flowchart explaining an operation of a structural domain predicting system according to a preferred embodiment of the 42^(nd) invention of the present application.

Steps S1201 through S1207 are the same as Steps S1081 through S1087 in FIG. 34, respectively. At Step S1208, a sequence fragment generated by cutting off the amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues at any portion of a region including a domain linker portion or a domain-linker existing position predicted at Step S1207 is predicted as a structural domain. At Step S1209, the result is outputted. The result output indicates, for example, predicted amino-acid sequences, position and size of the predicted linker sequence, etc.

A preferred embodiment of the structural domain predicting system of the 42^(nd) invention of the present application shown in FIG. 38 is realized by a computer similar to that shown in FIG. 21, which is provided with, for example, an F₁₁s(i) calculation part 1201, an F₁₁p(i) calculation part 1202, and an F₁₁(i) calculation part 1203, a secondary structure prediction part 1204, a region search part 1205, a domain linker existing position prediction part 1206 and a structural domain prediction part 1207 shown in FIG. 39. The F₁₁s(i) calculation part 1201, the F₁₁p(i) calculation part 1202, and the F₁₁(i) calculation part 1203, the secondary structure prediction part 1204, the region search part 1205, and the domain linker existing position prediction part 1206 are the same as the F₁₁s(i) calculation part 1091, the F₁₁p(i) calculation part 1092, and the F₁₁(i) calculation part 1093, the secondary structure prediction part 1094 and the region search part 1095 in FIG. 35, respectively. In the structural domain prediction part 1207, a sequence fragment generated by cutting off the amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues at any portion of a region including a domain linker portion or a domain-linker existing position predicted in the domain linker existing position prediction part 1206 is predicted as a structural domain.

FIG. 40 is a flowchart explaining an operation of a system for predicting a structural domain according to another preferred embodiment of the 42^(nd) invention of the present application.

Steps S1301 through S1309 are the same as Steps S1091 through S1099 in FIG. 36, respectively. Steps S1310 through S1311 are the same as Steps S1208 through S1209 in FIG. 38, respectively.

Another preferred embodiment of the structural domain predicting system of the 42^(nd) invention of the present application shown in FIG. 40 is realized by a computer similar to that shown in FIG. 21, which is provided with, for example, an A_(i) ^(k) identification part 1301, an S′_(Ai), S′_(AiAi+(m+1))(m) S′_(AiAi−(m+1))(m) calculation part 1302, an F₁₂s(i) calculation part 1303, and an F₁₂p(i) calculation part 1304, an F₁₂(i) calculation part 1305, a secondary structure prediction part 1306, a region search part 1307, and a domain linker existing position prediction part 1308 and a structural domain prediction part 1309 shown in FIG. 41. The A_(i) ^(k) identification part 1301, the S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) calculation part 1302, the F₁₂s(i) calculation part 1303, and the F₁₂p(i) calculation part 1304, the F₁₂(i) calculation part 1305, the secondary structure prediction part 1306, the region search part 1307 and the domain linker existing position prediction part 1308 are the same as the A_(i) ^(k) identification part 1101, the S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) calculation part 1102, the F₁₂s(i) calculation part 1103, and the F₁₂p(i) calculation part 1104, the F₁₂(i) calculation part 1105, the secondary structure prediction part 1106, the region search part 1107, and the domain linker existing position prediction part 1108 shown in FIG. 37. The structural domain prediction part 1309 is the same as the structural prediction part 1207 in FIG. 39.

The 43^(rd) invention of the present application provides a program for having a computer function as a system of the 42^(nd) invention of the present application.

The 44^(th) invention of the present application provides a method of constructing an amino-acid sequence database comprising a step for recording in a recording medium, concerning an amino-acid sequence with L₂ pieces (L₂ is an integer of 22 or more) of amino-acid residues, the amino-acid sequence of a sequence fragment generated by cutting off the amino-acid sequence at any portion of a region including a domain linker portion or a domain-linker existing position predicted by the method of the 36^(th) invention of the present application.

The 45^(th) invention of the present application provides a method of manufacturing a protein comprising a step for manufacturing a protein having the same amino-acid sequence as the structural domain predicted by the method of the 41^(st) invention of the present application.

The 46^(th) invention of the present application provides a method of analyzing a protein comprising a step for analyzing a protein having the same amino-acid sequence as the structural domain predicted by the method of the 41^(st) invention of the present application.

The 47^(th) invention of the present application provides a method of manufacturing a protein comprising designing a new multi-domain protein which is a domain linker peptide of the 40^(th) invention of the present application and is generated by connecting at least 2 protein fragments and manufacturing this multi-domain protein.

As above, the present invention is constituted by a first method using a neural network as in the 1^(st) to the 17^(th) inventions and a second method using statistical processing of occurrence frequency of an amino acid as in the 18^(th) to the 47^(th) inventions, and it is preferable that those methods are used in the complementary manner in identification of a linker. That is, even if a correct prediction result can not be obtained with the first method for a region to be predicted, there is a case that a correct answer can be derived if the second method is used, and vice versa. Also, by checking the results of the both, more reliable linker identification can be achieved. In any case, by combining these methods for various prediction candidates, a domain linker region in a protein can be correctly identified at the probability of about 65%.

The present invention will be explained in detail according to the embodiments. These embodiments are only for illustration of the present invention and do not limit the scope of the present invention.

[Embodiment 1] Characterization and Prediction of a Linker Sequence by Neural Network

Result

(a) Domain Sequence Analysis

First, it was examined if local sequence characteristics exist in a domain linker and if they can be extracted by a neural network. Segments derived from a multi-domain protein are classified into “linker sequence” and “non-linker sequence” depending on whether the amino-acid residue at its center is included in the domain linker or not (See the section on materials and methods). These classified sequences were used for learning of the neural network.

Optimization of Learning Conditions

Here, the conditions by which the neural network is efficiently trained were examined, and the size of the window (Table 2a) and the number of hidden units (Table 2b) were optimized so as to achieve the maximum learning effect.

The effect of the window size was evaluated by the proportion of the number of times of correct classification of linkers and non-linkers against the number of times of wrong classification. The result in Table 2a shows that the correct answer rate is slightly lowered with increase of the window size, while the correct answer rate of the linker sequence rises up to the window size 19 and then, gradually drops. This fact indicates that most of the characteristics of the sequences required for identification of the domain linker is included in 19 amino-acid residues. In the meantime, the drop in the correct answer rate of the linker sequence was found in the window size not less than 19 as with the drop in the correct answer rate of the non-linker sequence. This drop does not relate to the total of the characteristics of the sequences. That is because the once the window reaches a size enough to include all the characteristics of the sequence, the correct answer rate becomes constant but does not drop. We assumed that this drop was caused by the increase of the number of parameters brought into a larger window size, and the data set of the limited size would prevent the neural network from operating in the optimum state with the larger window size. Here, as the optimum condition, the window size of the 19 amino-acid residues was adopted.

We further examined the effect of the number of hidden units (Table 2b). In theory, the neural network in the case where there are not any hidden units can detect only independent contribution of each amino acid to the domain linker (first order features). When the hidden units are brought into, the ability of neural network to extract higher-level characteristics such as a relation between an amino-acid pair and the domain linker, for example, is improved (Qian & Sejnowski, 1988). However, in our research, increase of the number of hidden units did not remarkably improve the learning effect (Table 2b). The reason why the learning efficiency was not improved can be briefly explained by non-existence of higher-level characteristics in the linker sequence. However, as with the observation of the window size, the learning effect might be affected by reduction of the data size and too many parameters. Considering the calculation time or the fact that there is no effect even after introduction of many parameters, we decided to use the neural network with the number of hidden units set to 0 or 2 (zero means a two-layer network).

Effect of the Size of Data Set in Learning

In order to evaluate how the size of the data set affects the learning effect, we examined if the correct answer rate depends on the size of the training data set or not. The correct answer rate of linker sequence classification did not become flat even after the current data set got large (Table 2c), it is expected that the learning efficiency will be improved if more data is available. In other words, the data set used here is not sufficient to fully extract the characteristics of the domain linker. However, despite these limitations, the characteristics of the detectable linker sequences could be extracted using the neural network, which will be described below. Identification of linker sequence and non-linker sequence

The ability of the neural network to identify the linker and the non linker can be examined by distribution of output values of these neural networks (FIG. 1). We calculated output values of the linker sequences and the non-linker sequences and averaged these values over the smoothing window of 19 residues. The distribution of output values of the linker sequences were obviously different from the distribution of the output values of the non-linker sequences even though there are some overlaps (white and black bar graphs respectively in FIG. 1). The output values of the linker sequences tend to be higher (those with the output values distributing above 0.4 amount to 60.3% of the entire linker sequences), while the non-linker sequences and the in-domain loops indicate lower values (those with the output values of 0.2 or less are 59.1% and 53.3%, respectively).

Characterization of the Linker Sequence

The characteristics on the sequence extracted from the two-layer neural network can be visualized using the Hinton diagram (Rumelhart et al., 1986) (FIG. 2). In the case of the two-layer network, the respective weight parameter values are explained as contribution of a corresponding amino-acid residue to the difference between the linker sequence and the non-linker sequence (type of the amino acid and the position in the window). We observed that there is a high correlation between these weight parameters and the occurrence frequency of an amino acid at the respective position (no data shown). The Hinton diagram obviously indicates that proline is a strong determinant amino-acid residue. This fact matches the result of the amino-acid composition analysis (occurrence frequency of proline is 13.9% in the domain linker and 5.3% in the whole data). However, the characteristics depending on the position are also observed for the other residues whose content in the domain linker is almost equal to the content in the whole data set. For example, a histidine residue indicates obviously negative distribution at the C terminal, but this position corresponds to the C terminal of the domain linker, that is, the N terminal of the subsequent domain. Methionine, isoleucine, tyrosine and tryptophan also show negative distribution. In general, hydrophobic amino acids tend to show negative distribution, while hydrophilic amino acids contributes on the positive side. These results highlight the ability to efficiently extract characteristics of the sequence not known from the averaged amino-acid composition value with a neural network.

Proline-Rich Segment

As observed both in the amino-acid composition and the Hinton diagram, the domain linker has a characteristic of highly frequent occurrence of proline (the average number of proline residues in a domain linker is 1.65). However, some in-domain sequences also have portions with locally high proline content. Then, we assumed that the difference between the linker sequence and the non-linker sequence is the contents of other amino acids. We examined the characteristics of a short segment including at least 3 prolines in 9 residues (proline-rich segment). Most of the proline-rich segments belong to the in-domain region (50 in in-domain region against 26 in the domain linker), and most of them overlap the in-domain loop region. FIGS. 2 b and 2 c show all the proline-rich segments corresponding to the domain linker and the in-domain region, respectively, with the sequence of the 9 residues adjoining to the both ends. Interestingly, the domain linkers in the proline-rich segment and its adjoining sequences rarely include histidine (FIG. 2 b). On the other hand, in the sequence located in the domain, histidine occurs relatively frequently (FIG. 2 c). For example, though there are only 5 residues of histidine in the former sequence, while 38 residues are observed in the latter. Moreover, there are many histidine located at the C terminal of the sequence belonging to the in-domain region (against 13 of them on the half of the N terminal side, there are 25 on the half of the C terminal side). These evidences verify the characteristics found in the Hinton diagram and shows that histidine is an important clue in identification of the domain linker and the in-domain loop regions.

(b) Prediction of Domain Linker in Sequence of Protein

In this section, the ability of a neural network to predict a domain linker in an amino-acid sequence of a protein will be examined. First, a neural network having learned with the window size of 19 and the number of hidden units of 2 was used, and an output value of a protein to be examined was calculated. In order to convert the output of the neural network to prediction, the following three parameters were introduced: (1) Size of a smoothing window: The size of a window is determined, and output values exceeding this size are excluded (smooth). (2) Cut-off value: A peak is selected from the smoothed output values. (3) Threshold: A start position and an end position of a linker around the peak are determined.

Efficiency of Prediction

The efficiency of prediction was evaluated by measuring two values. One of them is a percentage indicating a proportion of a predicted region correctly assigned to a SCOP derived domain linker in all the predicted regions (specificity). (How many of predicted regions match those originally determined by SCOP as a domain linker). The other is a proportion of SCOP derived domain correctly predicted by the neural network in all the SCOP derived domain linkers (sensitivity). We examined the specificity and the sensitivity by changing two prediction parameters: size of the smoothing window and the cut-off value. The best prediction was achieved when the size of the smoothing window was fixed to 19 and the cut-off value to 0.5. Under these conditions, the specificity of the prediction was 58.8%, and the sensitivity of the prediction was 35.6% (FIGS. 3 a, b).

Next, we examined how the parameters of the cut-off value and the threshold value affect the prediction efficiency (Table 3). With increase of the cut-off value, the specificity rose, while the sensitivity dropped (FIGS. 3 a, b). In this way, the cut-off value parameter controls trade-off between the specificity and the sensitivity of prediction. On the other hand, when the threshold value is decreased, both the specificity and the sensitivity increase. This can be explained by allowance in assignment of candidate regions. This is controlled by the threshold value parameter; If the threshold value is low, the length of a predicted linker would be longer than the case where the threshold value is high. These results show that the cut-off value and the threshold value should be selected so that the balance between the specificity and the sensitivity should be desirable and that allowance in assignment of candidate regions should be desirable. In the following prediction, the value of 0.5 was used both for the cut-off value and the threshold value.

Linker Ranking

As mentioned in the section on materials and methods, we ranked the predicted candidate linkers according to their maximum smoothed output values. The correctly predicted candidate linkers were ranked at the first with preference (63.8% of all the correctly predicted candidate linkers ranked at the first), and there were few cases ranked lower (black bar graph in FIG. 4). Moreover, the candidate regions in the lower rank had wrong prediction in many cases (white bar graph in FIG. 4). These results support interrelation between our ranking and actual domain linker entity and show that selection of a sequence in the first rank can raise the specificity of prediction.

Comparison with Other Methods

In order to evaluate the ability of a neural network to predict a domain linker, comparison was made with other prediction methods. A standard domain linker prediction method has not been established yet, and a simple method using secondary structural prediction was compared with our method. Here, our method is based on an intuitive assumption that a domain linker is a long loop region, and the nature of those domain linkers were ranked according to the predicted length. Also, both the specificity and the sensitivity of prediction derived from DSC or PHD were lower than the respective values obtained by the neural network by at least 10%. Moreover, the length of the predicted loop has little relation with the nature of the domain linker (FIG. 3 c). These results with data shown in FIG. 2 indicate that the domain linker has a nature different from the in-domain loop region and that the nature can be distinguished by the neural network.

Example of Domain Linker Prediction

In FIGS. 5 a, b, an example of correct prediction by a neural network is shown. The neural network predicted one linker in collagenase (1fbl). This was correctly assigned to a SCOP derived domain linker. For serine tRNA synthetase (1 sesA), endo/exo-cellulose E4 catalyst domain and cellulose bound domain (1ft4B), in addition to a true positive linker, a false positive linker was predicted, but when only linkers in the first rank were selected, the false positive were eliminated (FIGS. 5 b, c). Pyroracemic acid decarboxylase (1pvdA) has three domains, and a linker dividing these domains was predicted from the first and the second rank linkers. Actually, the region extending from the amino-acid residue positions 183 to 193 (specified in PDB) (corresponding to 174-202 in FIG. 5) was not a domain linker originally, because the domain boundary defined in SCOP is located at the center of a 3-10 helix region. Despite this fact, the neural network identified this segment as a linker.

As shown in FIG. 3 b, some of the observed domain linkers were not correctly predicted by the neural network. Chitinase A (1ctm) is an example that prediction was not successful. In this case, a false signal was prevailing over a true signal corresponding to a SCOP derived domain linker (FIG. 6). For some short domain linkers, output of the neural network is a weak signal or it does not put out any signal.

Consideration

In an actual protein, since the size and structure of a domain linker are varied, definition for the domain linker is not always only one. For example, in addition to our definition, there can be definitions based on visual figures and movement of the domain. Therefore, classification of domain linkers into various types will be useful in comprehensive characterization of linker sequences. However, in our study, since the size of the data set was small, types of linkers were not analyzed in detail. Instead, a limited definition of domain linker (loop region adjacent to a domain which is structurally independent and is considered to be automatically folded) was employed. This narrow definition of domain linker seems to be suitable for recognition of characteristics of linkers by neural networks since it limits sequence patterns in the data set. However, as expected from Table 2c, if more structural data on multi-domain proteins are available in the future, the size of the data set will be larger and more detailed analysis will be enabled on more types of linker sequences.

Sequence patterns in a domain linker are suggested in the Hinton diagram (FIG. 2 a). In the learning process of the neural network, the characteristics of sequences are averaged for all the linker sequences used for learning. As a result, sequences specific to individual domain linkers become inevitably vague and will not appear on the Hinton diagram. Despite that, we found characteristic occurrence patterns for some amino acids including proline and histidine. This means that the linker sequences have common local characteristics. Considering that the amino-acid composition limits characteristics to distinguish a domain linker from other regions, this result should be surprising. Actually, the local characteristics of the sequence detected by our neural network had high interrelation with occurrence frequency at each amino-acid residue position in the window. As a whole, this discovery strongly suggests that the linker sequence is characterized not only by the contents of the amino acid but its occurrence pattern in the sequence.

The Hinton diagram shows that a histidine residue is mandatory as a proline residue in discriminating a domain linker from other regions (FIG. 2 a). Sequence analysis of a proline-rich segment explains a difference in occurrence frequency of histidine between the domain linker and other regions, especially with in-domain loop (FIGS. 2 b, c). Our prediction succeeded probably and partially because of recognition of the histidine residue by the neural network. In FIGS. 2 b, 2 c, since the proline-rich segment has high proline content, an output value of the neural network is higher than general. However, the proline-rich segment including histidine tends to show a lower output value, and there is a strong correlation between the histidine content and the neural network output value (2 b, 2 c). Referring to other examples, the sequence of ifbl is (164-198, position of residue in PDB/65-99 for the position used in FIG. 5 a) including two proline-rich segments and (253-284, 154-185). The former sequence is characterized by high histidine content, while the latter does not include histidine. The neural network gives a smoothed output value lower than 0.46 to the former and a value higher than 0.62 to the latter. In this way, the position of a domain linker is correctly determined.

Assumption of a structural information amount accumulated in a local sequence is derived from prediction efficiency. In the case of blind prediction, that is, prediction without any information is roughly estimated as follows. Assume the case where a protein of amino-acid residue 300 made of two domains and the average domain size is 150. In our data set, the average domain linker size is 12.2 residues. Also, the minimum domain size is 60 residues, and when assuming that 60 residues on both ends of the protein sequence are not included in our calculation, the blind prediction gives a correct answer rate of 7% (12.2/300−60×2). On the other hand, in our study, the prediction efficiency of the neural network was 35.6% for the sensitivity and 58.8% for the specificity (FIGS. 3 a, 3 b). In any case, improvement in efficiency from the blind prediction to the prediction by neural network (about 30 to 50%) is attributable to the structural information accumulated in the local sequence. In this way, this assumption indicates that the local sequence information can be a useful clue in detecting a domain linker. However, it also indicates that a major portion of the domain linker information is not local at the same time, and to further improve prediction, information which is not local should be taken in. Despite that, our neural network is one of rare means which can be used for detecting a virtual domain linker in sequences of a protein and has a possibility to contribute to structural and functional analysis of a large protein.

Materials and Methods

Preparation of Data

Multi-domain proteins whose structure was analyzed with resolution of 2.5 Å or more and classified in SCOP database were selected from PDB (Protein Data Base). Duplication of sequences were eliminated according to the BLAST standard with the value of e of 10·−70 (The most homologous sequences were 49% (1hyxH and 2fbjH).).

The domain linker was defined as follows. First, as determined by DSSP, a domain linker is considered to be a loop region made of at least 4 residues and include domain boundary defined by SCOP. Most of actual domain linkers corresponded to a single loop region, but in a few exceptions, it had plural loop regions in which short secondary structural elements are scattered. In these cases, not all the loop regions corresponding to them were considered as domain linkers but the only loop region was first made as a domain linker. Therefore, at the next stage of visual inspection, in order to encompass all the domain linkers, we expanded the determined region manually. Then, all the structures of the domains whose range was determined by the above defined domain linker were visually inspected. Since the SCOP definition of domain is based on the evolutionarily stored structural units, it does not match our necessary condition on the domain structure. Actually, in some multi-domain proteins, it was obviously observed that domains closely adhere to each other (e.g.: D amino-acid oxidase). Also, it seems that these SCOP defined domains can not be folded to their original structure when isolated. Moreover, we found that this ambiguity in the domain definition or domain linker definition accompanying it prevents progress of learning by a neural network. Thus, we visually examined the structure of each protein and selected only domain linkers adjoining the domain considered to take its original structure by individually and autonomously being folded. As a result, we obtained 99 domain linkers (SCOP derived) existing in 74 types of multi-domain protein.

Neural Network

The neural network is a method for pattern recognition, and layered feed forward networks relate to input and output. The network is optimized using the back propagation algorithm so as to obtain desired input/output relations. This process is called as learning or training (for detailed explanation, see documents by Rumelhalt). In our study, in order to classify sequence segments, a neural network having a single hidden layer (FIG. 7) and a neural network having no hidden layer were used. In the learning process of the neural network, a sequence segment coded by binary system was given as an input pattern, classification of these sequence segments into the linker sequence or the non-linker sequence was made as output of 1 or 0, respectively. In this learning process, we used momentum term set to 0.9 (for predicate, Rost & Saunder was followed), and parameters of bias and weight were set in a range at random [−0.3, 0.3]. Magnitude of learning (that is, a step width of gradient drop) was made as 0.001 for the first 100 learning stages and 0.005 for the next stage. In all the stages, a correct answer rate of sequence classification was checked, and when the correct answer rate reached a peak value, the learning was stopped. In checking the correct answer rate of classification, it was considered that the case where the output value (predicted value) of neural network is not less than 0.5, it was classified to the linker sequence, while the value not more than that was classified to the non-linker sequence, and the correct answer rate was examined.

The back propagation algorithm was written in the C language, and Fujitsu's VPP700E super computer at Wako Campus, Riken was used.

Training

In order to extract domain linker information, we trained the neural network so that it discriminates domain linkers from non-linker sequence segments. Sequence segments of the length equal to a given window size were moved from the N terminal to the C terminal of a protein sequence and collected. Each of the sequence segments was classified to the linker sequence or the non-linker sequence according to whether the residue at its center is a part of the domain linker or not (FIG. 8). We proceeded with training using the linker sequence and the non-linker sequence at the proportion of 1:3. With this proportion, the linker and the non-linker can be discriminated most efficiently. The sequences were clearly coded. That is, each amino acid in the sequence segment was converted to 21-bit binary numbers (FIG. 9). Each bit corresponds to 20 standard amino-acid residues with the remaining corresponding to the one that can not specify an amino acid or that is not a standard amino acid. For example, the code of alanine is 100000000000000000000. In the classification of sequence, the linker was coded as 1, while the non-linker as 0.

Test

For evaluation of learning efficiency of neural network, two methods were used. One is a single testing method, and data sets are merely divided into 2 groups, one of which is used for training and the other for testing. The proportion of data set for training to that for testing was set at 4:1. The second method is a 10-fold Jackknife test. In this method, the data set was divided into 10, in which data from 9 groups was used for learning of neural network, while the other was used to examine learning efficiency of data. This process was repeated 10 times till all the groups were used for the test.

Prediction of Domain Linker by Neural Network

The first stage of linker prediction is to calculate an output value of neural network for sequence of the examined protein. Using the optimized 19-residue window, we calculated the output value of each residue in the protein sequence, and the value was made as a characteristic of the amino acid at the center of the window. Since this raw output value is extremely varied along the sequence of a protein, reliable prediction of the domain linker region was prevented. Thus, an averaged output value of the 19 residues (averaging over the 9 residues before and after) was used for the domain linker (For optimization of smoothing of this window, see the section on results).

We made the following three-stage prediction. (1) First, we assume the minimum size of a domain and ignored 60 residues at both ends of the protein. (2) We selected all the peaks from smoothed output values larger than a cut-off value. Then, a region close to the peak value having a smoothed output value larger than a threshold value was defined as a virtual domain linker (note that the cut-off value is larger or equal to the threshold value). (3) Lastly, the predicted domain linkers were ranked according to the peak value of smoothed output value (FIGS. 5, 6, for example). In order to evaluate prediction using this method, the Jackknife test was carried out for the data set of multi-domain proteins. Since various sequence patterns were required for training of neural network, we used the data set selected by the e value of 10⁻⁷⁰ for training. However, this data set includes sequences similar to each other, and it might affect evaluation of prediction. Then, we eliminated the sequences having the identity of full length smaller than the e value of 10⁻²⁰ (this corresponds to the fact that more than 25% of the sequences are identical) (Shown in Table 1). In the end, prediction efficiency was calculated for the set of 66 multi-domain proteins including 87 domain linkers.

[Embodiment 2] Setting of Threshold Value of Output Value (g(X)) of Neural Network

For the protein sequence of the test data used in Embodiment 1, a window of 19 residues was taken and the sequence fragment of the length of 19 residues was given to the neural network to calculate an output value (a value of 0.0-1.0 was obtained, and this becomes the output value for the residue at the center of the window.). The window was sequentially displaced from the N terminal to the C terminal of the protein, and output was calculated at each position. In preparing distribution, cases are classified depending on whether the residue at the center of the window is a domain linker or not, and the respective distributions were obtained. The neural network used here has three layers, and the number of the hidden units was 2. Also, distribution was obtained by the jackknife test. The results is shown in FIG. 16.

[Embodiment 3] Preparation of Domain Linker Database

For 86593 amino-acid sequences registered in SWISSPROT whose structure is totally unknown, prediction was made according to the method in Embodiment 1. The used neural network has three layers, and the number of hidden units was 2.

Also, prediction was (independently) made with (10 in total) neural networks optimized using 10 pieces of learning data (prepared for the Jackknife test), and the obtained 10 smoothing output values were averaged. In this averaging, the length of the smoothing window (smoothing window length) was set at 19 residues. For this average value (of 10 neural networks), an assumed linker domain was determined under the condition of the cut-off value=0.95, threshold value=0.5. The terminal regions (60 residues) of the protein were all included in the prediction. The linker domains were not ranked here (all the prediction domains were taken).

The amino-acid sequences predicted as linker sequences were stored in the hard disk.

Appendix

Discussion on theoretical/methodological backgrounds has an essential meaning in setting appropriate problems (and problem solution), which can not be avoided. However, it can be an independent subject of discussion and it will be discussed separately in an appendix. Here, theoretical framework for the neural network and concrete designing of methodology based on it will be described.

A. Neural Network

A. 1. Theoretical Framework of Neural Network

The neural network shall have the following neural model as its basic component (FIG. 10). ${y = {\tau\quad(u)}},\quad{u = {w_{0} + {\sum\limits_{i = 1}^{n}\quad{w_{i}x_{i}}}}}$ where, τ is a sigmoid function represented as follows: ${\tau\quad(u)} = \frac{1}{1 + {\mathbb{e}}^{- u}}$ and it takes a value of [0, 1]. In this neuron model, x_(i) is the i-th input signal coming from an axon of another neuron, w_(i)(i=1, . . . , n) is a degree that the input signal is strengthened by the synapse, −w₀ is a threshold value, y represents an output of the neuron. That is, the input signal is weighted according to the connection strength, and whether the total u (corresponding to the internal potential of a neuron) is larger or smaller than the threshold value determines active state of the neuron (if y is 1, it is in the activated state, while if it is 9, it corresponds to the inactivated state). The connection strength can have an arbitrary real number value, and a positive value corresponds to an excitatory synapse and a negative value for an inhibitory synapse. Also, in the case of 0, it can be interpreted that there is no synapse connection.

In the neural network, neuron models are connected to each other to form a network. Here, a hierarchical feed-forward network is used. That is, neurons are arranged in the layered state so as to construct a network in which signals are transmitted from the previous layer to the next layer only in one direction. With this type of network, a neuron output in an output layer (output signal) is determined uniquely for a signal (input signal) given to a neuron in an input layer. In this sense, it can be considered as a kind of signal converter. When the connection strength/threshold value is changed, a function represented by the network is also changed, but it was proved that selection of an appropriate value can realize a non-linear continuous function ([Funahashi, 1989]). In learning, a connection strength/threshold value which can realize correct input/output relations are sought, but they can be automatically determined if the error back-propagation learning method [Rumelhart, 1986] is followed.

Referring to the three-layer neural network to be actually used in this study (FIG. 11), the error back-propagation learning method will be explained. For the input layer/hidden layer/output layer, n pieces/m pieces/1 piece of neurons are prepared, respectively. Assuming J≡[0, 1], the input x and the output z of the network and the output y of the hidden layer are defined as follows: x≡{x|x=(x ₁ , . . . , x _(n)), x _(i) ε J} y≡{y|y=(y ₁ , . . . , y _(m)), y _(i) ε J} z≡{z|z=(z ₁ , . . . , z _(l)), z _(i) ε J}

At this time, the input/output relations of the network can be understood as a function from J^(n) to J^(l): h=g·f Here, f is a function from J^(n) to J^(m) realized by the hidden layer. f(x) = (f₁(x), ⋯  , f_(m)(x)) ${f_{j}(x)} = {\tau\quad\left( {w_{0\quad j} + {\sum\limits_{i = 1}^{n}\quad{w_{ij}x_{i}}}} \right)\quad\left( {{j = 1},\cdots\quad,m} \right)}$ Also, g is a function from J^(m) to J^(l) realized by the output layer. g(x) = (g₁(x), ⋯  , g_(l)(x)) ${g_{k}(x)} = {\tau\quad\left( {v_{0\quad k} + {\sum\limits_{j = 1}^{m}\quad{v_{jk}x_{j}}}} \right)\left( {{k = 1},\cdots\quad,l} \right)}$ In leaning, in the error back-propagation method, an index called as an error is used as follows: $E \equiv {\frac{1}{2}{\sum\limits_{x \in X}\quad{{{h(x)} - {\mathbb{d}(x)}}}^{2}}}$ Here, d(x)=(d₁(x), . . . , d₁(x)) is a correct output for the input x. X is a set of inputs x. This error E represents how far the neural network output is separated from an ideal output, and the smaller value means that it is the closer to desirable pattern identification. In learning, a dynamical system is set so as to decrease this value. $\left\{ \begin{matrix} {\frac{\mathbb{d}v_{jk}}{\mathbb{d}t} = {- \frac{\partial E}{\partial v_{jk}}}} & \left( {{j = 0},\cdots\quad,m,\quad{k = 1},\cdots\quad,l} \right) \\ {\frac{\mathbb{d}w_{ij}}{\mathbb{d}t} = {- \frac{\partial E}{\partial w_{ij}}}} & \left( {{i = 0},\cdots\quad,n,\quad{j = 1},\cdots\quad,m} \right) \end{matrix}\quad \right.$ In this dynamical system, since it can be confirmed that an error E does not increase against time, if started with an appropriate weight as an initial value, the track of the dynamical system is retained at a minimum point of the error E in the end, and a desired weight can be gained. Here, the right side of the equation of the dynamical system can be concretely obtained from the definition equation of the error E as follows: $\left\{ {\begin{matrix} {\frac{\partial E}{\partial v_{jk}} = {\sum\limits_{x \in X}\quad{{\delta_{2\quad k}(x)}{f_{j}(x)}}}} & \left( {{j = 0},\cdots\quad,m,\quad{k = 1},\cdots\quad,l} \right) \\ {\frac{\partial E}{\partial w_{ij}} = {\sum\limits_{x \in X}\quad{{\delta_{1\quad j}(x)}x_{i}}}} & \left( {{i = 0},\cdots\quad,n,\quad{j = 1},\cdots\quad,m} \right) \end{matrix}{where}\left\{ \begin{matrix} {{\delta_{2\quad k}(x)} \equiv {\left\lbrack {{h_{k}(x)} - {d_{k}(x)}} \right\rbrack{h_{k}(x)}\left( {1 - {h_{k}(x)}} \right)}} \\ {{\delta_{1\quad j}(x)} \equiv {\left\{ {\sum\limits_{k = 1}^{l}\quad{{\delta_{2\quad k}(x)}v_{jk}}} \right\}{f_{j}(x)}\left( {1 - {f_{j}(x)}} \right)}} \end{matrix} \right.} \right.$ From this, the dynamical system equation can be described in more concrete form as follows: $\left\{ \begin{matrix} {\frac{\mathbb{d}v_{jk}}{\mathbb{d}t} = {- {\sum\limits_{x \in X}\quad{{\delta_{2\quad k}(x)}{f_{j}(x)}}}}} & \left( {{j = 0},\cdots\quad,m,\quad{k = 1},\cdots\quad,l} \right) \\ {\frac{\mathbb{d}w_{ij}}{\mathbb{d}t} = {- {\sum\limits_{x \in X}\quad{{\delta_{1\quad j}(x)}x_{i}}}}} & \left( {{i = 0},\cdots\quad,n,\quad{j = 1},\cdots\quad,m} \right) \end{matrix}\quad \right.\quad$ Moreover, when the left side is substituted by a difference, the following recurrence formula is derived: $\left\{ \begin{matrix} {{\Delta\quad{v_{jk}(t)}} = {{- \Delta}\quad t{\sum\limits_{x \in X}\quad{{\delta_{2\quad k}(x)}{f_{j}(x)}}}}} & \left( {{j = 0},\cdots\quad,m,\quad{k = 1},\cdots\quad,l} \right) \\ {{\Delta\quad{w_{ij}(t)}} = {{- \Delta}\quad t{\sum\limits_{x \in X}\quad{{\delta_{1\quad j}(x)}x_{i}}}}} & \left( {{i = 0},\cdots\quad,n,\quad{j = 1},\cdots\quad,m} \right) \end{matrix}\quad \right.$ When the weights w_(ij), V_(jk) are made to evolve with time according to this recurrence formula, it can finally reach the minimum value of the error E. The above has been the principle of operation of the error back-propagation learning method. A.2. Improvement of Learning Algorithm Achieved in This Study

According to the above recurrence formula, all the weights w_(ij), v_(jk) in the network can optimized in principle. However, some problems occur if this learning is to be executed actually. First, it is essential to take a time width Δt small in a sense to improve the accuracy of convergence solution, but as a result, a change amount per time gets small and the number of learning times becomes enormous. Therefore, the value of Δt should be large to some extent in practice, which means the convergence gets worse. Also, once the error E reaches a minimum value which is not the smallest (local minimum), it can never get out of the current algorithm. Such a big problem still remains.

In order to solve these problems, in this study, an inertial term is added to the above recurrence formula. That is, the weight is represented by w and the following recurrence formula is set: ${\Delta\quad{w(t)}} = {{{- \Delta}\quad t\frac{\partial E}{\partial w}} + {\alpha\quad\Delta\quad{w\left( {t - 1} \right)}}}$ Here, 0<α<1, and the closer to 1 is α, the larger is the effect of the inertial term. In the normal method, if a large value is taken for Δt, w fluctuates around the minimum value of E, and learning would not converge. On the other hand, since the new recurrence formula is changed in the direction to suppress fluctuation by the action of the inertial term, convergence of learning can be maintained even for a large Δt. Also, by decreasing fluctuation, converging speed can be considerably improved. The effect of the inertial term is also demonstrated when overcoming fine irregularity on the E curved face (when seen as a function of the weight w). Therefore, by adjusting the combination of Δt and α, the problems of increase in the number of learning times and trap by the local minimum can be avoided to some extent. As a result, after trial and error of conditions, this study was fixed to α=0.9, and Δt was set according to the given network. A.3. Computer Environment

In carrying out the error back-propagation learning method, the algorithm was described in the program language C, and calculation was executed using the super computer VPP700E at RIKEN. TABLE 1 Used multi-domain protein and domain linker PDB chain Domain linker(s) Protein name 1a2o_B 139-157 CheB methylestense 1a3q_B 219-229 Nucler factor-κB p52 1a5t 164-168 Delta prime 1a8p  93-100 NADPH: ferdexin oxidoreductase 1ao6 528-574 Formate dehydrogensse H 1ahr_B 139-144 Abrin-A 1ahw_A 138-145 Hemoglobin-based blood substrate 1ais_B 1197-1207 Transcription Initiation factor IIB 1amm 81-88 γ B-crystallin 1acq_B 129-138 Nitrite reductase 1acx_B 123-134, 330-344 Ascorbate oxidase 1axi_B 129-134 Growth hormone receptor 1bfd 175-186, 329-354 Bezoylformate decarboxylate 1bia 269-274, 60-68 Bira bifunctional protein 1bif 242-250 6-phosphofructo-2-kinase/fructose-2,6- bisphosphatase 1cfb 709-720 Drosophils neuroglim 1cg2_A 211-214, 323-329 Carboxypeptidate O2 1chm_B 157-160 Crestine aminohydrolase 1cly 457-463 Cryia(A) 1ckm_A 236-242 mRNA capping ensyme 1ctn 132-158 Chitinase A 1dot 333-344 Ovotransferrin 1ecf_A 243-252 Glutamino phosphodbosylpyrophosphate amidotransferrse 1cfi 210-221, 306-312 Elongation factor Tu 1cfv_A 188-196, 205-211 Electron transfer flavoproteis 1etp_B 87-95 Cytochrome C4 1eut* 401-407, 502-505 Sialidase 1fbl 251-285 Collagenase 1fie_A 184-197, 500-517, 627-632 Coagulation factor XIII 1fml_A 189-208 Methionyl-tRNA fMax formyltransferase 1fnb 152-163 Ferrebxin: NADP+ oxidorediotane 1fnf 1233-1239, 1325-1330, 1415-1420 Fibronectin 1gof 148-159, 534-545 Galactose oxidase 1hrf 104-109 CD2 1hsf_A 180-185 Class 1 histocompatibility antigen AW68.1 1hyx_H 112-119 Immunoglobulin 6x9 1hyy_L 107-113 Immunoglobulin 6x9 1iak_A 78-87 MHC class II I-AK 1lik_B 93-97 MHC class II I-AK 1lib_B 202-209, 98-106 Type 1 interleukin-I receptor 1jmc_A 289-304 Replication protein A 1nhq 116-127, 312-326 NADH peroxidue 1ncp_A 119-123 Single-chain antibody fragment 1pem_B 493-499, 582-585 Cyclodextrin glucanotransferase 1pgs 136-141 Peptide-N(4)-(N-acetyl-β-D-glucosaminyl) asparagine amidase 1plq 118-134 Proliferating cell nuclear antigen 1pox_B* 179-198, 365-372, 544-563 Pyruvate oxidase 1pvd_A 341-366 Pyruvate decarboxylase 1opa 173-222, 353-339, 780-787 Chitobiase 1req_B 455-494 Methylmalonyl-CoA mutase 1rpl 328-337 Pancreatic lipase related protein I 1aes_A  99-113 Seryl-tRNA synthetase 1sfe 80-94 ADA O6-methylguanine-DNA methyltransferase 1sox_B 310-347 Sulfite oxidase 1taq 289-295 Taq DNA polymerase 1tcr_A 116-123 α, β T-cell receptor 1tf4_B 445-462 Endo/exo-cellulase B4 catalytic domain and cellulose-binding domain 1uag 296-303 UDP-N-acetylmurasoyl-L-alanine/:D-glucamate ligase 1vcr_A 90-95 Vascular cell adhesion molecule-1 1vcde_B 180-187, 396-416 Pl-Sced 1yge 145-150 Lipoxygenase-1 1xcq 85-91 Interrcellular achesion molecule-2 2bb2* 81-88 β-B2-crystallin 2fbj_H* 117-124 Ig*A Fab fragment 2gep 140-155, 328-346, 419-425 Sulfite reductase bernoprotein 2hft 106-112 Human tissue factor 2pis 224-237, 99-112 Phthalate dioxygenase reductase 2pol_B 116-125 pol III (β subunit) 2ram_B* 185-195 Transcription factor NF-κB p65 3fru_C* 178-182 Neonstale Fe receptor 3grs 161-170, 355-368 Glutachione reductase 3lad_B* 155-166, 341-348 Dihydrolipoamide dehydrogenase 8flb_C* 106-113 Fab fragment from human immunoglobulin IgG1 8ruc_G 146-154 Ribulose-1,5-bisphosphaste carboxylase/oxygenate

A protein chain whose structure (crystal structure with resolution of 2.5 Angstrom or more) is known and sequence is non-redundant (BLAST e value is at the level of 10⁻⁷⁰) is shown. Asterisks (*) indicate protein chains having a sequence similar to the other protein chains included in this data set (because the BLAST e value is less than 10⁻²⁰). These sequences were used for learning but they were not used for evaluation of domain linker prediction. Identification of 4-letter PDB codes and chains are on the left column. The first and the last residues of the SCOP derived domain linkers are on the center column. The names of the protein chains are on the right column. TABLE 2 Conditions and learning efficiency Linker [%] Non-linker [%] (a) Window size.^(a) Window size  3 27.8 (1.2) 91.8 (0.9)  5 34.1 (2.2) 88.3 (2.0)  7 43.9 (3.5) 84.4 (2.0)  9 46.3 (2.6) 85.4 (1.7) 11 51.1 (2.8) 84.0 (1.4) 13 55.7 (1.8) 82.1 (1.6) 15 58.1 (1.3) 82.2 (0.8) 17 59.6 (1.0) 81.5 (1.1) 19 61.7 (1.5) 80.6 (1.0) 21 60.9 (2.2) 79.9 (1.2) 23 58.9 (1.8) 79.9 (1.0) 25 57.7 (1.4) 80.6 (1.1) 27 56.4 (1.1) 80.2 (1.4) 29 56.9 (1.6) 79.2 (1.0) 31 55.6 (3.0) 79.8 (1.4) 33 54.1 (1.3) 80.3 (1.3) 35 54.7 (2.1) 78.6 (0.8) (b) Number of hidden units.^(b) Hidden units  0^(c) 60.9 (0.4) 82.4 (0.5)  2 61.7 (1.5) 80.6 (1.0)  3 61.1 (1.7) 81.6 (0.9)  4 61.5 (1.6) 80.7 (0.7)  5 63.6 (1.4) 79.3 (1.3) 10 63.3 (2.1) 79.4 (1.2) 15 62.8 (0.9) 79.2 (1.1) 20 64.1 (1.4) 79.5 (0.9) (c) Training data set size.^(d) Dataset size^(e)  0.1 39.0 (1.8) 75.5 (0.6)  0.2 50.4 (1.9) 70.8 (1.7)  0.3 47.5 (1.5) 79.3 (1.3)  0.4 52.1 (1.9) 75.7 (1.0)  0.5 53.2 (2.0) 79.0 (1.1)  0.6 52.4 (1.7) 80.8 (1.0)  0.7 56.2 (1.8) 79.8 (1.5)  0.8 57.9 (0.8) 81.3 (1.0)  0.9 60.3 (2.1) 80.0 (0.9)  1.0 61.7 (1.5) 80.6 (1.0)

The following conditions: window size (a), the number of hidden units (b) and the size of training data set (c) were changed and learning was executed using the three-layer neural network. By calculating the correct answer rates of the linker sequence and the non-linker sequence using a single test method (See Materials and methods), the learning efficiency was evaluated. The sequence segment with the output value of neural network larger than 0.5 was predicted as a linker sequence. The others were predicted as a non-linker sequence. Learning was started with at-random initial parameters and executed 10 times independently. The correct answer rates of the linker and the non-linker sequences were averaged among 10 times of independent learning and indicated in Table. The standard deviation is shown in the parentheses.

The number of a hidden units was set to 2. The ^(b)window size was 19 residues. ^(c)0 indicates that there is no hidden layer. The ^(d)window size and the number of hidden units were 19 and 2, respectively. The proportion of ^(e)training data set to the initial size. TABLE 3 Influence of threshold value and cut-off value on prediction efficiency Thresh- Cut-off old 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 (a) Specificity. 0.9 63.6 — — — — — — — — 0.8 72.7 52.6 — — — — — — — 0.7 72.7 57.9 50.0 — — — — — — 0.6 81.8 63.2 62.5 56.5 — — — — — 0.5 81.8 63.2 65.6 58.7 58.8 — — — — 0.4 81.8 63.2 65.6 60.9 60.8 55.2 — — — 0.3 81.8 63.2 65.6 60.9 60.8 55.2 51.6 — — 0.2 81.8 63.2 65.6 60.9 60.8 58.6 54.7 54.6 — 0.1 81.8 63.2 65.6 60.9 62.8 60.3 56.3 56.1 56.1 (b) Sensitivity. 0.9 8.1 — — — — — — — — 0.8 9.2 11.5 — — — — — — — 0.7 9.2 12.6 18.4 — — — — — — 0.6 10.3 13.8 23.0 29.9 — — — — — 0.5 10.3 13.8 25.3 32.2 35.6 — — — — 0.4 10.3 13.8 25.3 33.3 36.8 37.9 — — — 0.3 10.3 13.8 25.3 33.3 36.8 37.9 39.1 — — 0.2 10.3 13.8 25.3 33.3 36.8 40.2 41.4 42.5 — 0.1 10.3 13.8 25.3 33.3 37.9 41.4 42.5 43.7 43.7

Using the smoothing window of 19 residues, the domain linker in a protein sequence was predicted, and the prediction efficiency in the first rank prediction region was evaluated by the 10-fold jackknife test. The two values used for evaluation (specificity (a) and sensitivity (b)) were the same as those in FIGS. 3 a and 3 b. TABLE A 1 2 Group 1 w(i, j) 0 0.203088 0.540009 1 0.073914 −0.34164 2 0.668079 0.503217 3 0.045715 −0.61632 4 0.111587 −0.17979 5 0.182084 −0.0401 6 −0.3307 0.707415 7 0.219901 0.514386 8 −0.09145 −0.14363 9 −0.60034 0.021658 10 −0.05301 0.191661 11 0.708844 0.486389 12 0.010888 −0.26662 13 −0.41839 −0.50119 14 −0.46904 0.190709 15 0.326836 −0.12006 16 −0.08283 −0.35478 17 −0.00795 −0.22021 18 0.119587 0.215764 19 0.031814 0.236334 20 0.101783 0.26889 21 0.241188 −0.28814 22 −0.41516 −0.15032 23 0.656729 0.145216 24 −0.16417 −0.26117 25 −0.24376 0.412418 26 0.227849 −0.42203 27 −0.09348 0.408046 28 0.153017 0.374756 29 0.209754 −0.22188 30 −0.20783 −0.30559 31 0.206758 −0.00058 32 0.409745 0.683895 33 −0.13617 −0.1969 34 −0.66977 −0.25687 35 −0.17179 −0.03489 36 −0.02782 0.299192 37 0.050957 −0.59742 38 −0.17204 −0.31799 39 0.078222 0.21067 40 0.179898 −0.12665 41 0.08324 0.370715 42 0.211288 −0.01238 43 0.169011 0.01512 44 0.384231 0.359081 45 −0.86572 0.271657 46 0.157363 −0.05606 47 −0.42993 0.088111 48 0.125666 0.315909 49 0.08278 0.772704 50 0.347408 −0.03607 51 0.00797 −0.47078 52 −0.03288 0.238103 53 0.540945 0.694973 54 −0.22537 −0.25544 55 −0.37341 −0.41868 56 −0.20714 −0.05525 57 −0.06712 0.261499 58 0.198648 −0.38155 59 −0.14564 −0.2884 60 0.386566 0.29794 61 −0.21057 0.088406 62 −0.108 0.621091 63 0.189822 −0.04068 64 0.375172 −0.24881 65 0.280784 0.350218 66 −0.32876 −0.03357 67 −0.07806 0.01148 68 −0.26105 −0.01629 69 0.387278 0.437011 70 0.386287 0.923562 71 0.185638 0.239484 72 0.199535 −0.69202 73 −0.28438 0.395351 74 0.756292 0.665594 75 −0.12696 −0.15193 76 −0.23617 −0.7661 77 −0.09949 −0.05336 78 0.04634 0.137315 79 −0.23178 0.00718 80 −0.03971 −0.50462 81 −0.31114 0.530159 82 −0.23345 −0.0257 83 −0.02918 0.592355 84 −0.23439 0.085195 85 0.13202 −0.17814 86 0.261043 0.189141 87 −0.04655 −0.13789 88 −0.12989 −0.06276 89 −0.51844 0.145467 90 0.295651 0.301802 91 0.290119 0.991052 92 0.04461 0.390948 93 −0.01422 −0.78845 94 0.134781 −0.19037 95 0.474398 0.989826 96 0.091282 −0.37682 97 −0.869 −0.45437 98 −0.23552 −0.13247 99 0.191084 0.418961 100 −0.6409 0.101467 101 0.421567 −0.65302 102 0.284741 0.052028 103 −0.11986 0.01357 104 0.285669 0.029401 105 −0.25297 −0.03396 106 0.014272 −0.00808 107 0.231999 0.211252 108 −0.18804 −0.12474 109 0.087 −0.12682 110 −0.22814 −0.02755 111 0.244127 0.367347 112 0.784543 0.520689 113 0.149655 0.784079 114 −0.23133 −0.41153 115 0.004895 −0.04649 116 0.384475 0.859132 117 −0.04573 −0.03756 118 −0.62681 −0.74889 119 0.197454 −0.3442 120 0.291285 0.407792 121 −0.58478 0.206976 122 0.238565 −0.33292 123 0.097992 0.357675 124 0.092729 0.226479 125 0.550985 −0.09568 126 −0.06271 −0.18487 127 −0.10729 0.01074 128 0.210412 0.347196 129 −0.62222 −0.26147 130 −0.25796 −0.27077 131 −0.12156 0.071659 132 −0.01946 0.129441 133 0.891879 0.355866 134 0.564503 0.630488 135 −0.23093 −0.34267 136 0.023624 −0.03566 137 0.565664 0.561007 138 0.084232 −0.48613 139 −0.9251 −0.81282 140 −0.16212 −0.41277 141 0.231087 0.098628 142 −0.38896 −0.16256 143 −0.32491 −0.2981 144 0.182849 0.078623 145 −0.05575 0.314276 146 0.185952 0.307593 147 −0.09747 −0.26393 148 0.17624 −0.35769 149 0.23492 0.080185 150 −0.31363 −0.38283 151 0.058098 −0.10503 152 −0.16272 0.214434 153 −0.05524 −0.03954 154 0.622912 0.623841 155 0.645335 0.620295 156 0.040316 −0.1983 157 −0.20348 0.433101 158 0.372777 0.352405 159 −0.14011 −0.51238 160 −0.92278 −0.79862 161 −0.54901 0.149817 162 −0.01294 0.571202 163 0.021641 −0.62211 164 −0.69912 0.157707 165 0.574073 0.142712 166 0.322987 0.005772 167 0.618337 0.269614 168 0.265902 −0.15868 169 0.157827 −0.20402 170 0.028886 0.051689 171 −0.13465 −0.55666 172 0.258128 −0.57963 173 0.213903 0.300525 174 0.006395 −0.05051 175 0.527014 0.397299 176 −0.08341 0.818489 177 0.096983 −0.249 178 0.206032 0.230246 179 0.477328 0.691801 180 −0.41699 −0.3035 181 −0.57723 −0.9143 182 −0.45925 −0.01211 183 −0.17188 0.349711 184 −0.22653 −0.24533 185 −0.78692 0.092476 186 0.334388 0.844046 187 0.855526 −0.18564 188 0.368002 0.885076 189 0.195082 −0.13708 190 0.059913 0.063141 191 0.096481 0.305493 192 0.192202 −0.73329 193 −0.13854 −0.19136 194 −0.31815 0.416714 195 0.367023 −0.38544 196 0.286686 0.570619 197 0.3929 0.595546 198 −0.22844 0.259292 199 0.25547 0.457686 200 0.234665 0.970347 201 −0.62163 −0.47735 202 −0.67553 −0.99274 203 0.107656 −0.25714 204 0.205029 0.16812 205 0.097486 −0.3854 206 −0.53177 −0.08877 207 0.380016 0.534568 208 0.45693 0.153908 209 0.32634 0.806303 210 −0.17631 −0.14437 211 −0.0411 −0.06376 212 0.23951 0.045609 213 −0.20442 −0.74475 214 0.073167 −0.24842 215 0.189712 −0.08041 216 0.005198 0.025968 217 0.101933 0.568057 218 0.399463 0.662669 219 −0.40578 0.0777 220 0.125337 0.431644 221 0.411373 0.486051 222 −0.78261 −0.31995 223 −1.22404 −0.95589 224 0.08699 −0.27955 225 −0.09821 0.621336 226 0.042753 −0.45847 227 −0.11693 −0.36604 228 0.113745 0.476587 229 0.173725 0.270702 230 0.56185 0.323922 231 0.06301 0.001923 232 −0.31059 −0.20397 233 0.324997 0.018771 234 −0.09743 −0.68422 235 −0.01322 0.030533 236 −0.08388 −0.1557 237 0.189697 0.088263 238 0.16064 0.551251 239 −0.01986 0.568367 240 −0.39143 0.136758 241 0.440537 0.034732 242 0.392792 0.330706 243 −0.39351 −0.05948 244 −1.17077 −0.88137 245 −0.38548 0.012554 246 0.345199 0.274505 247 −0.6181 −0.20843 248 −0.13399 −0.33174 249 0.104228 0.356645 250 0.301217 0.126347 251 0.448494 0.163406 252 −0.15862 −0.1854 253 −0.21489 −0.11044 254 0.197129 0.263244 255 −0.06038 −0.33234 256 0.098681 0.009518 257 −0.0969 −0.03526 258 0.281643 0.483559 259 0.010048 0.919913 260 0.435673 −0.0995 261 −0.31441 0.097275 262 −0.02226 0.388633 263 0.33509 0.696228 264 −0.25108 −0.34716 265 −0.90538 −1.08562 266 0.141516 −0.00531 267 0.487108 0.025541 268 −0.02694 −0.26978 269 −0.20007 −0.10958 270 0.222975 0.143381 271 0.102519 0.318553 272 0.189818 0.425075 273 0.066414 0.278496 274 −0.13978 −0.1304 275 0.609217 0.031532 276 −0.50278 −0.19433 277 0.411463 −0.42302 278 −0.27966 0.028935 279 0.694426 0.149943 280 0.627737 0.671108 281 0.038077 0.042256 282 −0.2655 0.03135 283 0.102474 0.110377 284 −0.09849 0.322938 285 −0.27829 0.017574 286 −1.02283 −0.92786 287 −0.01837 0.121062 288 0.237061 0.034332 289 −0.48873 0.299139 290 −0.27517 −0.27876 291 −0.14755 0.175789 292 0.345262 0.030499 293 0.014736 0.527607 294 −0.16378 0.161211 295 −0.33541 0.062575 296 −0.00391 0.403422 297 −0.3426 −0.27167 298 0.18699 −0.24662 299 0.108613 −0.18845 300 0.508756 0.380611 301 0.731858 1.000181 302 0.114055 −0.36009 303 0.082556 0.026083 304 −0.06738 0.119676 305 0.039332 −0.04198 306 −0.11006 −0.15986 307 −0.88112 −0.63456 308 0.155289 −0.01426 309 0.109575 0.469614 310 −0.20505 0.036813 311 −0.18698 −0.49412 312 −0.04873 0.168336 313 0.025702 0.05031 314 −0.11124 0.407873 315 0.047223 −0.23643 316 0.102958 −0.12006 317 0.674179 0.260172 318 −0.41698 0.249571 319 −0.30771 0.010681 320 0.1453 −0.55156 321 0.163701 0.425897 322 0.530241 0.817036 323 −0.03604 −0.03902 324 0.106241 0.052858 325 −0.20991 0.031123 326 0.196667 0.281562 327 −0.06811 −0.28679 328 −0.56776 −0.75427 329 0.299402 −0.33616 330 0.168059 0.031208 331 0.352322 −0.30052 332 −0.17216 −0.38732 333 −0.27658 −0.0851 334 −0.3196 −0.10739 335 0.195742 0.206005 336 0.010308 −0.20822 337 −0.07463 −0.09805 338 0.039709 0.252356 339 −0.22698 0.105322 340 −0.28974 −0.08327 341 −0.01719 −0.19148 342 0.340217 0.47778 343 0.855064 1.043365 344 0.002245 −0.05562 345 0.048565 −0.15503 346 −0.1008 −0.0194 347 0.161311 0.317004 348 0.006362 −0.20268 349 −0.74142 −0.45124 350 −0.03248 −0.04255 351 0.031161 0.041716 352 0.277543 −0.07988 353 0.176521 −0.59229 354 −0.23469 −0.0568 355 −0.03005 0.274288 356 0.100855 0.513823 357 0.168584 −0.16726 358 0.076166 0.125704 359 0.42765 0.140564 360 −0.42414 0.382035 361 −0.22894 −0.0216 362 −0.34243 −0.0781 363 0.216098 −0.07901 364 0.551773 1.2368 365 −0.09594 −0.11456 366 −0.0232 −0.20889 367 −0.26975 0.117923 368 0.608954 −0.04884 369 −0.27152 −0.11366 370 −0.69291 −0.63739 371 −0.16959 −0.00889 372 −0.05624 0.24408 373 0.406214 −0.35149 374 −0.02814 −0.31822 375 −0.11775 −0.26461 376 0.172854 0.105598 377 0.349553 −0.02751 378 0.131891 0.065268 379 0.120444 0.100008 380 0.458291 0.502448 381 0.443249 −0.41384 382 −0.0834 −0.48195 383 0.064858 0.058266 384 0.168691 −0.13751 385 0.756834 0.961917 386 −0.1738 −0.20047 387 −0.13101 −0.18184 388 −0.11993 −0.00069 389 0.290256 0.081142 390 −0.35059 0.049965 391 −0.16127 −0.74512 392 −0.1623 0.031976 393 0.211564 0.25765 394 0.24337 −0.09502 395 −0.1533 −0.31831 396 0.174432 −0.15268 397 0.076752 0.13494 398 0.057971 0.313684 399 0.187533 0.027739 Group 1 v(j) 0 3.2501 1 −5.21239 2 −6.36906

TABLE B 1 2 Group 2 w(i, j) 0 0.372319 1.012758 1 −1.341 0.650946 2 0.158913 0.96759 3 −1.00242 0.502232 4 −0.16249 0.109527 5 −0.04493 −0.0061 6 0.147951 0.828177 7 0.257626 1.502491 8 −0.42083 −0.05306 9 0.04632 −0.55298 10 0.5877 −0.12828 11 −0.07568 1.047878 12 −0.66223 0.201755 13 0.518818 −2.15565 14 −0.04026 −0.27853 15 −0.0951 −0.62544 16 −0.30661 −1.02384 17 −0.83816 0.543225 18 0.837488 −0.21466 19 1.31166 0.003249 20 −0.09556 0.160277 21 −0.22429 0.005239 22 −1.08283 0.177379 23 1.85618 0.677984 24 0.550711 −0.92495 25 0.61898 −0.53054 26 −1.25602 0.431499 27 0.836531 0.709338 28 0.172603 1.268029 29 0.544312 −0.54946 30 0.439839 −1.27576 31 −0.9683 1.0389 32 −0.26756 0.404665 33 0.186216 −0.57616 34 −0.59601 −0.53179 35 −1.17389 0.801059 36 −0.36422 −0.0952 37 0.006947 −0.96672 38 −0.36351 −0.47753 39 0.545638 0.025779 40 −0.36275 0.127718 41 0.124485 0.920747 42 −0.03199 −0.13435 43 −0.09835 −0.15629 44 1.171092 1.222355 45 0.643286 −1.22703 46 −0.46178 0.200579 47 −0.65874 0.238926 48 1.396822 −0.07879 49 0.926215 −0.10695 50 −0.78907 0.7949 51 −0.41946 −0.18274 52 0.804891 −0.43246 53 0.006097 0.887291 54 −0.44191 0.150472 55 −0.7983 −0.32103 56 −0.56179 −0.41367 57 −0.31169 0.380215 58 −0.33279 0.190591 59 −0.72536 −0.47715 60 0.585753 0.099597 61 −0.80454 0.564453 62 0.453927 0.248351 63 −0.08668 −0.04731 64 0.318061 −0.84727 65 0.374398 0.757071 66 −2.0298 1.146123 67 0.394106 −0.39591 68 0.07358 −0.70301 69 −0.68274 1.441549 70 −0.46442 1.017186 71 −0.71161 1.377589 72 −0.11208 −1.47182 73 0.767579 0.188171 74 0.272972 0.790575 75 0.029222 −0.75555 76 −0.9388 −0.33266 77 0.563326 −0.28903 78 0.953385 −0.61675 79 −0.45069 −0.52235 80 −0.371 −0.16591 81 0.170516 0.027167 82 0.329378 0.473275 83 1.230148 0.066737 84 0.107705 −0.01789 85 −0.11121 −0.46777 86 0.611088 0.969042 87 −0.75603 0.690166 88 0.546101 −0.57099 89 −0.03037 −0.54039 90 1.474246 0.332466 91 0.204416 1.429161 92 −0.14068 0.514587 93 −1.41905 0.199062 94 0.216501 −0.44243 95 0.03831 0.868207 96 0.296135 −0.56985 97 −1.38752 −0.76682 98 0.206328 −0.63806 99 1.174771 0.124625 100 −0.41639 −0.10495 101 −0.27166 −0.54396 102 −0.16883 −0.72151 103 0.407663 0.218976 104 −0.55194 0.169801 105 −0.23534 0.006364 106 0.226047 −0.80968 107 0.516791 1.117572 108 −0.974 0.409229 109 −0.48793 0.055412 110 −0.85389 0.437169 111 0.949932 −0.6671 112 0.5633 1.540877 113 0.528601 0.635268 114 −1.12373 −0.47794 115 −0.2104 0.019839 116 0.747487 0.255723 117 −0.11946 −0.26685 118 −1.35075 −0.86309 119 0.053518 −0.768 120 −0.17937 0.765414 121 −0.15649 −0.48113 122 −0.96195 0.414535 123 0.683285 −0.98484 124 0.640423 0.074378 125 0.848435 −0.88792 126 0.005374 0.052965 127 0.490916 −0.9179 128 0.325312 1.215089 129 −0.10178 −0.26361 130 −0.71463 0.56387 131 0.197467 −0.27329 132 −0.9659 0.649583 133 1.535152 0.41254 134 1.051094 −0.00066 135 −0.24396 −0.58386 136 0.003446 −0.25114 137 0.558898 0.715059 138 0.3027 −0.71344 139 −0.84002 −2.00214 140 0.121945 −0.44956 141 −0.39661 0.56633 142 −0.91024 0.092194 143 −0.20685 −0.3164 144 −0.42944 0.76597 145 0.601729 1.575967 146 0.37399 −0.24323 147 −0.1151 0.022806 148 0.099057 −0.49125 149 0.563675 0.427817 150 1.040476 −2.26792 151 −0.88453 0.579925 152 0.461455 0.21274 153 0.320121 0.002335 154 −0.03817 1.98842 155 0.889309 0.400192 156 −1.20325 0.185965 157 −0.16815 0.58407 158 −0.02384 0.760548 159 −0.4854 0.116441 160 −0.76274 −1.17413 161 −0.42853 0.136514 162 −0.25117 0.788685 163 −0.81991 −0.60464 164 1.093789 −1.29857 165 0.593176 −0.62777 166 0.042685 1.250965 167 0.289241 0.201878 168 −0.10597 0.136875 169 −0.13298 −0.12669 170 −0.25962 0.58148 171 −0.22509 −0.9229 172 0.092411 −0.32242 173 0.049033 0.970155 174 −0.12387 −0.12311 175 1.123553 1.601295 176 1.605461 0.525174 177 −0.33026 −0.47233 178 1.329003 −0.77797 179 0.797318 1.285923 180 −0.82889 −0.61139 181 −1.17017 −1.09782 182 −0.06474 −0.59703 183 0.020001 −0.69653 184 −0.44051 −0.5325 185 −0.91604 0.388778 186 0.313204 0.834129 187 0.446538 0.391983 188 −0.1375 1.045966 189 −0.27902 0.168854 190 0.213499 −0.5981 191 0.524226 0.29399 192 −1.876 0.114566 193 0.331433 −1.34881 194 0.330727 0.165592 195 0.638544 −0.81778 196 0.393752 1.091602 197 1.259493 −0.05325 198 −0.22225 −0.32938 199 0.31073 0.566817 200 0.601091 1.423425 201 −0.42536 −0.39793 202 −0.82215 −1.75331 203 −0.48023 0.198024 204 −0.63781 0.1369 205 0.191438 −0.6548 206 −0.98536 0.31134 207 0.138424 0.77689 208 −0.37989 1.705708 209 0.497788 0.001009 210 −0.14845 −0.1907 211 −0.46655 −0.15832 212 0.609589 0.646876 213 −0.80251 −0.72485 214 −1.53593 0.878273 215 0.021097 −0.08568 216 −0.29809 0.00275 217 1.435665 0.654431 218 0.905449 0.519054 219 −0.84481 0.443573 220 0.818234 0.359483 221 1.039553 0.620431 222 −0.71191 0.12189 223 −1.55452 −2.1478 224 −0.20686 −0.87571 225 −1.0579 0.255759 226 −0.19342 −0.27488 227 1.367741 −1.18942 228 1.015088 0.373095 229 1.039317 0.363051 230 0.741473 0.944602 231 −0.02939 0.050053 232 0.460047 −0.65877 233 0.498954 0.414528 234 0.007725 −2.18768 235 0.268561 0.838417 236 −0.20237 0.169613 237 −0.07271 0.875462 238 −0.03225 1.018183 239 −0.35942 1.141722 240 −0.20693 −0.23387 241 −0.59737 1.700581 242 0.020339 1.171419 243 0.089375 −1.81856 244 −1.79811 −1.14135 245 0.549497 −0.52375 246 0.111344 0.262793 247 −1.18526 0.798752 248 −0.63376 −0.30982 249 1.30076 −0.29873 250 0.888363 0.25456 251 1.300921 0.228738 252 0.012754 −0.24326 253 −0.33606 −0.24743 254 0.977908 −0.18158 255 −0.04509 −0.71121 256 −0.23876 −0.06482 257 −0.02321 −0.73439 258 0.099253 1.016878 259 −0.0417 1.372833 260 −0.06396 −0.07946 261 0.383551 −0.26515 262 1.326307 −0.06171 263 −0.28182 1.62259 264 0.502595 −1.252 265 −1.13057 −2.3503 266 −0.09228 −0.30353 267 −0.59805 0.410668 268 −0.47716 −0.29089 269 −0.58518 0.211163 270 −0.55333 1.1767 271 0.094785 0.800725 272 1.324693 −0.31817 273 −0.06387 0.00125 274 −1.50464 1.020169 275 1.245549 −0.24367 276 −0.67602 −0.3428 277 0.528288 −0.59713 278 0.024628 0.118675 279 1.055138 0.026115 280 0.859912 1.269743 281 1.258145 −0.71006 282 −0.50994 0.291778 283 0.958029 0.299932 284 0.689574 0.024824 285 −1.07561 0.471378 286 −1.91763 −0.62226 287 −1.25017 0.766226 288 −0.16323 −0.10854 289 0.638055 −0.82443 290 −0.53975 −0.33419 291 0.758639 −0.15319 292 0.594179 0.570446 293 −0.92564 0.960015 294 −0.13725 0.237896 295 0.289032 −0.08296 296 −0.30306 0.836385 297 −0.33999 −1.03909 298 −1.37385 0.605332 299 0.31271 −0.55184 300 0.665469 0.580574 301 1.942278 0.893087 302 −0.6842 0.414846 303 −0.05879 0.018329 304 0.803861 −0.19056 305 −0.61378 0.550721 306 0.892449 −1.32746 307 −1.32872 −0.86773 308 −0.38608 0.126183 309 −0.70359 1.03929 310 0.415473 0.029884 311 −0.26547 −0.04058 312 0.819376 −0.25439 313 −0.30077 0.664709 314 0.612671 −0.62634 315 0.170665 −0.03717 316 0.249139 0.094595 317 0.584117 0.50475 318 −0.16904 −1.10622 319 −1.16225 0.454448 320 −1.04308 0.580959 321 0.947568 −0.24702 322 0.46843 1.812657 323 −1.00285 0.836803 324 0.153991 0.082174 325 0.749477 0.101108 326 0.127364 0.671505 327 −0.28706 −0.61516 328 0.318896 −1.41377 329 0.677223 −0.06426 330 −0.22088 −0.69879 331 0.596426 −1.05072 332 0.291061 −0.35945 333 −0.73066 1.099099 334 −0.88041 0.896239 335 0.808179 −0.88718 336 0.188898 −0.23301 337 −0.21541 0.373246 338 −0.08762 0.914606 339 0.118484 −0.20604 340 −0.24408 0.251664 341 −0.37165 0.461679 342 0.089567 0.603273 343 1.496688 1.466543 344 −0.05072 −0.25358 345 0.313925 −0.41294 346 0.053316 0.749362 347 −0.74389 0.411311 348 −0.49302 −0.25245 349 −0.94967 −0.96243 350 0.851304 −0.41661 351 0.345168 −0.70767 352 −1.01369 0.879443 353 0.01378 −0.3087 354 0.701879 −0.79491 355 0.572887 −0.42668 356 −0.08216 −0.10615 357 −0.02387 0.181898 358 0.877753 −0.2666 359 0.324874 1.059339 360 −0.8376 0.46615 361 −0.44131 0.541288 362 −0.08335 0.157274 363 0.066947 −0.27572 364 1.137957 2.041129 365 0.300565 −0.50854 366 0.238039 −0.37083 367 0.020584 −0.02529 368 1.333457 −0.61684 369 0.182297 −0.42132 370 −2.02979 −0.38779 371 0.556706 0.002565 372 0.639737 −0.94327 373 1.380703 −1.56491 374 −0.56515 0.013118 375 −1.1856 0.670355 376 −0.72614 0.44601 377 −0.5484 −0.1112 378 0.003803 −0.1694 379 0.393805 −0.70671 380 1.49297 1.159131 381 −0.70885 0.204981 382 −0.64565 0.045964 383 0.469698 0.142748 384 −1.23385 1.509698 385 1.029039 2.167971 386 −1.13576 −0.61285 387 −0.02462 −0.83687 388 −0.00175 −0.07921 389 0.756253 −0.37463 390 0.543368 −1.08814 391 −0.35125 −0.78552 392 −0.86242 −0.03181 393 −0.29751 0.254151 394 0.818977 −0.73301 395 −0.45858 0.213372 396 0.597384 −0.43315 397 −0.80248 1.288501 398 −0.19609 −0.08565 399 −0.1102 −0.11805 Group 2 v(j) 0 6.492565 1 −12.1013 2 −12.758

TABLE C 1 2 Group 3 w(i, j) 0 1.004024 −0.11681 1 −0.46811 0.090162 2 1.279157 −0.19382 3 −0.30628 −0.37219 4 −0.14028 −0.15035 5 −0.2048 0.133447 6 0.512491 −0.01194 7 0.63078 −0.28511 8 −1.02646 0.842553 9 −0.62444 −0.12475 10 0.472281 −0.81161 11 0.306864 0.63061 12 −0.16558 −0.18881 13 −1.06502 0.597906 14 0.272965 0.034676 15 −0.57892 0.63626 16 −0.37242 −0.97125 17 −0.38615 0.08074 18 0.07122 0.149479 19 0.755653 0.223882 20 0.268192 −0.15909 21 −0.2046 −0.13816 22 −0.0853 0.070648 23 0.892944 0.704875 24 0.146346 −0.791 25 0.170655 0.145587 26 −0.83426 0.209631 27 0.698428 0.389035 28 0.785289 −0.54712 29 −0.64214 1.009625 30 −1.29797 0.402818 31 0.039817 0.07894 32 0.61725 0.618425 33 −0.40266 0.478541 34 −0.26985 −1.16237 35 0.080986 −0.04654 36 −0.3608 0.160113 37 −0.55668 −0.37711 38 −0.18491 −0.69771 39 0.479744 −0.2725 40 0.062613 0.333443 41 0.672461 −0.19654 42 0.209104 0.186025 43 0.614902 −1.10572 44 1.134287 −0.16237 45 0.234847 −0.71651 46 0.686253 −0.37688 47 −0.79735 0.253434 48 1.015096 −0.3108 49 0.75879 0.263073 50 −0.0865 0.683639 51 −1.03435 0.206723 52 0.438253 −0.18217 53 0.236015 0.894676 54 −0.3544 −0.4623 55 −0.45392 −0.58569 56 −0.79325 0.684121 57 −0.2426 0.542804 58 −0.27223 −0.73384 59 −0.58165 −0.34843 60 0.115739 0.34983 61 0.260375 0.091938 62 0.398343 0.233472 63 0.152738 −0.15343 64 0.106383 −0.18249 65 0.728098 0.290297 66 −0.336 −0.28259 67 0.389201 −0.54929 68 −0.90409 0.453672 69 0.426757 0.538328 70 0.859309 0.930478 71 0.493995 0.151622 72 −1.0182 0.026609 73 0.651485 −0.20388 74 0.299455 0.396555 75 −0.29099 −0.22434 76 −0.94351 −0.11843 77 0.086563 −0.31442 78 −0.58351 0.355236 79 −0.53903 −0.57365 80 −0.16276 −0.71377 81 −0.11496 0.259748 82 0.12623 −0.41488 83 0.654674 0.100566 84 0.202198 0.211111 85 0.396006 −0.44005 86 0.663665 −0.0656 87 0.31313 −0.71306 88 0.514124 −0.77319 89 −0.22935 −0.27617 90 0.372575 0.740254 91 0.264275 1.078486 92 0.734117 0.652704 93 −0.68451 −0.22033 94 0.646702 −1.08029 95 0.990196 −0.11291 96 −0.32513 0.084341 97 −0.98137 −0.37282 98 −0.06306 0.428022 99 −0.13921 0.666978 100 −0.33762 −0.2141 101 −0.75245 0.753085 102 0.240273 −0.50352 103 −0.46653 0.39949 104 0.288331 0.417016 105 0.157725 0.135273 106 0.041753 0.092251 107 0.147789 0.186064 108 −0.9583 0.389773 109 0.373819 −0.49031 110 −0.42647 −0.19777 111 0.074202 0.616781 112 0.85043 0.857786 113 0.801465 −0.1226 114 0.030552 −0.5568 115 −0.29244 0.129129 116 0.584148 0.274931 117 −0.67056 0.165075 118 −0.87811 −0.9584 119 −0.50145 0.3473 120 0.799634 −0.10651 121 −0.03293 −0.39887 122 −0.04378 −0.67914 123 0.512023 −0.21647 124 0.78011 −0.10479 125 −0.00434 0.080991 126 0.188919 0.126331 127 0.197557 0.291773 128 0.42123 0.474027 129 −0.20866 −1.27725 130 −0.01356 −0.33619 131 −0.69968 0.582187 132 0.746966 0.125134 133 1.226108 0.133789 134 0.97259 −0.38866 135 −0.34146 −0.10497 136 −0.1678 −0.08602 137 0.39727 0.354463 138 −0.28935 0.310911 139 −1.31728 −0.72753 140 −0.215 −0.49316 141 0.432077 0.240804 142 −0.44211 −0.04486 143 −0.24664 −0.21749 144 −0.384 0.746762 145 0.686701 −0.12241 146 0.604833 0.519606 147 0.028166 0.287481 148 0.230852 −0.74712 149 0.368127 0.111856 150 −0.78333 −0.24773 151 0.062378 −0.1906 152 −0.14611 0.093142 153 0.210439 0.507843 154 0.321131 0.956007 155 0.110984 1.129606 156 0.107698 −1.24675 157 0.122315 0.099841 158 0.455235 0.512434 159 −0.20897 −0.25961 160 −1.28075 −0.83038 161 −0.70688 −0.01295 162 0.689556 −0.28957 163 −1.0605 −0.08662 164 −0.05183 −0.32778 165 0.138294 0.317154 166 0.690033 −0.20754 167 0.510691 0.722132 168 0.289157 −0.22229 169 0.491521 −0.69939 170 0.06764 0.069653 171 −0.22002 −1.14676 172 −0.19473 −0.37497 173 −0.06457 0.140806 174 0.199647 0.144141 175 0.611402 0.010185 176 0.714286 0.638965 177 −0.77794 0.223457 178 0.139636 0.68296 179 1.172761 0.140248 180 −0.0795 −0.37251 181 −1.96427 −0.07096 182 −0.29195 −0.4436 183 0.028678 0.002673 184 −0.85479 0.000457 185 0.588077 −1.12861 186 −0.15922 1.248564 187 0.469895 0.412343 188 0.631877 0.818812 189 −0.1148 −0.13338 190 0.200086 0.294969 191 −0.33438 0.279061 192 −1.39349 0.160891 193 −0.05931 −0.05823 194 −0.66762 0.309202 195 0.104839 −0.35225 196 0.383507 0.803746 197 0.785425 0.906542 198 −0.07847 −0.12003 199 0.797546 −0.26118 200 0.682677 0.157548 201 −0.26744 −1.14416 202 −1.89516 −0.70392 203 −0.24401 −0.72596 204 −0.09464 0.206922 205 −0.40848 −0.78097 206 −0.12837 −0.3297 207 1.248755 −0.49065 208 1.0963 0.327233 209 0.547934 0.515923 210 −0.00832 0.035282 211 0.264242 −0.05309 212 −0.45123 −0.14118 213 −1.06745 −0.23329 214 0.867713 −1.50369 215 0.055919 −0.08365 216 0.359941 −0.40581 217 0.843012 −0.03312 218 0.871078 −0.05446 219 0.231425 −0.65604 220 −0.60082 1.656698 221 0.741195 −0.484 222 −1.12097 0.070659 223 −1.57549 −0.739 224 0.125157 −0.63895 225 −0.26437 1.142433 226 −0.68609 0.406983 227 −0.3541 0.422875 228 0.368056 0.733312 229 0.772901 0.400143 230 1.266734 0.492368 231 −0.08848 −0.17902 232 −0.35565 0.361561 233 0.412036 0.36919 234 −1.38829 −0.05899 235 0.199105 0.341281 236 −0.14544 0.177778 237 0.230189 0.031033 238 1.093614 0.193318 239 0.089004 0.2415 240 −0.67759 0.609855 241 0.693831 0.288255 242 1.478346 −0.42766 243 −0.56983 −0.03365 244 −0.75739 −2.06033 245 −0.54685 0.325194 246 −0.15521 0.448378 247 −0.77507 0.039176 248 0.295671 −0.53819 249 0.137191 0.69708 250 1.265553 −0.03233 251 0.996088 0.047599 252 0.296115 0.124905 253 0.656914 −0.88604 254 0.673108 −0.07355 255 −0.22631 −0.66768 256 −0.26885 0.831377 257 −0.28345 −0.05506 258 0.412438 −0.03448 259 0.492824 0.651686 260 0.06211 −0.33171 261 −1.15656 0.539162 262 0.203141 0.665158 263 1.14548 0.098247 264 −0.20716 −0.83843 265 −1.47386 −0.84748 266 0.336032 −0.8546 267 0.046214 0.289208 268 −0.62178 0.272184 269 −1.0668 0.692154 270 0.585225 −0.35786 271 1.103219 0.381376 272 0.788853 −0.31099 273 −0.17332 0.11223 274 −0.36651 0.130302 275 −0.01107 0.850712 276 −0.78903 −0.11641 277 0.252346 −0.10787 278 0.051208 −1.04722 279 0.012939 0.44276 280 0.799078 0.990284 281 −0.12157 −0.25303 282 −0.6013 0.245574 283 0.801383 −0.41376 284 0.820691 0.280123 285 0.220597 −0.36296 286 −1.20743 −1.21132 287 0.209962 −0.41378 288 −0.13633 −0.08769 289 0.031633 −0.19123 290 −0.85594 0.307278 291 0.144258 0.536252 292 0.881918 0.140548 293 0.645941 −0.5031 294 0.262111 −0.25639 295 0.232752 −0.13855 296 0.821786 −0.02311 297 −0.35687 −0.52199 298 −0.57111 0.773281 299 −0.41137 0.000981 300 0.502704 0.000514 301 1.692603 0.859202 302 0.132702 −0.4733 303 0.133975 −0.47971 304 0.272025 0.216747 305 −0.69142 0.335123 306 0.036624 0.239196 307 −1.68968 −0.00324 308 −0.66983 0.502012 309 0.26929 −0.19238 310 −0.34765 0.144632 311 −0.1718 0.41873 312 −0.08424 0.276866 313 −0.06493 0.006073 314 0.296196 0.081631 315 0.213089 0.010418 316 0.277913 −0.18024 317 0.766437 −0.06923 318 −0.20061 −0.18397 319 −0.35767 0.668918 320 −0.10929 −0.19674 321 −0.49762 1.314274 322 1.382855 0.509434 323 −0.12215 −0.29356 324 −0.68324 0.233548 325 0.282519 −0.26659 326 0.333216 −0.14135 327 0.211095 −0.82173 328 −1.42946 0.264724 329 −0.20359 −0.33235 330 0.228757 −0.18728 331 0.03754 0.205635 332 0.533825 −0.64817 333 −0.15608 0.136506 334 0.28726 −0.2505 335 0.078657 0.074542 336 −0.26028 0.280049 337 0.378086 −0.23957 338 0.693161 0.428142 339 0.703408 −1.45698 340 0.055301 0.280806 341 0.261535 −0.41249 342 0.794976 −0.38405 343 1.476265 1.181076 344 −0.83566 1.164971 345 −0.11267 −0.64174 346 0.161657 −0.56449 347 −0.68506 0.955127 348 0.220672 0.021767 349 −0.80982 −0.51308 350 −0.43622 0.048359 351 0.177509 −0.72598 352 −0.06145 0.651952 353 0.104504 −0.30518 354 −0.4938 0.706649 355 1.244981 −0.59617 356 0.145796 0.655866 357 −0.09185 0.226241 358 −0.08146 0.41829 359 0.776445 0.553408 360 0.167289 −0.01266 361 0.178662 −0.33074 362 0.576612 −0.55005 363 0.68667 −0.57215 364 2.122255 1.240154 365 0.003564 −0.58875 366 −0.71716 0.522011 367 −0.39368 −0.07848 368 −0.47967 −0.42041 369 −0.82776 0.481101 370 −1.37468 0.029261 371 −0.44288 −0.13636 372 0.074483 −0.29835 373 0.270493 0.184273 374 −0.3248 −0.04902 375 −0.22869 −0.31825 376 0.53391 −0.31017 377 0.159034 −0.05819 378 −0.07994 −0.24517 379 0.441122 −0.71809 380 0.330793 0.425578 381 −0.25331 −0.59126 382 −0.42893 0.273508 383 0.128794 0.38432 384 0.387389 −0.2666 385 1.895239 0.821941 386 −0.04176 −0.0793 387 −0.45132 0.055102 388 0.245882 −0.99002 389 0.377565 0.3972 390 −0.25513 −0.56847 391 −0.70826 −0.57396 392 −0.59585 0.137021 393 0.259558 −0.09784 394 0.359762 −0.29718 395 −0.65384 0.626671 396 −0.12596 −0.14852 397 −0.29259 1.007973 398 0.159272 −0.22977 399 −0.01964 −0.00385 Group 3 v(j) 0 4.927978 1 −10.0383 2 −8.69324

TABLE D 1 2 Group 4 w(i, j) 0 0.226206 0.260618 1 −0.03189 −0.21085 2 0.52392 0.253769 3 −0.58775 0.144325 4 −0.16012 −0.10151 5 −0.5876 0.160045 6 0.279785 0.170879 7 0.614079 0.133685 8 0.26442 −0.16267 9 −0.21516 −0.3054 10 −0.00563 0.265494 11 0.647089 0.220283 12 0.305374 −0.00304 13 −0.36445 −0.49975 14 −0.11731 −0.23575 15 0.105189 −0.10202 16 −0.00651 −0.25626 17 −0.42596 0.331674 18 0.404073 −0.16025 19 −0.08717 0.179923 20 0.708343 −0.22046 21 −0.07864 −0.12575 22 −0.34943 0.195537 23 0.034287 0.655379 24 −0.42965 −0.00546 25 0.107411 −0.16686 26 −0.05767 −0.56613 27 0.388889 −0.03338 28 0.189386 0.487292 29 −0.43662 0.505805 30 −0.66538 −0.07828 31 −0.10182 0.381624 32 0.477485 0.469298 33 −0.1221 −0.05404 34 −0.59457 −0.26283 35 −0.0667 −0.28251 36 0.304533 −0.51715 37 −0.18205 −0.38069 38 −0.07302 −0.41194 39 0.084175 −0.1292 40 0.057405 −0.1273 41 0.574239 −0.19857 42 0.224194 −0.28833 43 −0.10035 0.242529 44 0.067762 0.738802 45 −0.07279 −0.24517 46 −0.05828 −0.17968 47 −0.40972 −0.20438 48 0.426567 0.245457 49 0.246013 0.442851 50 0.002712 0.534569 51 −0.52675 −0.15654 52 0.336688 0.24233 53 0.660565 0.714213 54 −0.10583 −0.16144 55 −0.64909 −0.16975 56 −0.35712 0.021783 57 −0.06857 0.210661 58 −0.03571 −0.06023 59 −0.34567 −0.08102 60 0.437818 −0.21721 61 −0.1234 −0.21718 62 0.371482 0.200683 63 −0.185 0.045429 64 0.372766 −0.33343 65 0.443291 0.38682 66 −0.15587 −0.14673 67 −0.39113 0.217053 68 −0.5104 0.073388 69 0.368508 0.303623 70 0.401565 0.443822 71 0.094551 0.425654 72 −0.30696 −0.50007 73 0.212491 0.250549 74 0.647447 0.59292 75 −0.06403 −0.10011 76 −0.60491 −0.36691 77 −0.00165 −0.37519 78 −0.11133 0.174124 79 −0.15852 −0.29007 80 −0.29174 −0.16216 81 0.35238 −0.08113 82 −0.07812 −0.20428 83 0.478907 0.301337 84 0.118891 0.042763 85 0.311708 −0.42851 86 0.344308 −0.04858 87 −0.33733 0.14195 88 −0.3803 0.071193 89 −0.11079 −0.18699 90 0.512906 0.045017 91 0.112473 0.546731 92 0.692633 −0.03599 93 −0.52251 −0.48746 94 0.155087 0.112051 95 0.283569 0.861488 96 −0.17636 0.113391 97 −0.92332 −0.30994 98 −0.40473 0.100675 99 0.179164 −0.0087 100 −0.42849 0.116815 101 −0.09302 −0.02803 102 0.258587 −0.40879 103 −0.01173 0.190435 104 0.269888 0.199216 105 −0.13057 −0.00024 106 0.13323 −0.18031 107 0.40161 0.217409 108 −0.37429 −0.02991 109 −0.12809 −0.08833 110 −0.10525 0.139387 111 0.153842 0.389767 112 0.471743 0.065518 113 0.479758 0.398661 114 −0.47459 −0.52318 115 0.068511 −0.00164 116 0.466496 0.656382 117 −0.3289 0.278205 118 −1.27668 −0.26538 119 −0.3896 −0.11537 120 0.42313 −0.28983 121 0.051053 −0.27401 122 0.046605 −0.31091 123 −0.08976 0.108483 124 0.504903 −0.23784 125 0.056955 0.246386 126 0.252427 0.052024 127 0.085108 −0.15773 128 0.180587 0.545152 129 −0.16724 −0.31275 130 −0.18565 −0.30719 131 0.128329 0.069173 132 0.139314 0.17111 133 0.593687 0.370089 134 0.669274 0.457737 135 −1.0218 −0.02481 136 0.020255 −0.06774 137 0.730902 0.172791 138 0.028517 −0.13515 139 −1.17361 −0.5307 140 −0.28338 −0.10519 141 0.480372 −0.33086 142 −0.26465 −0.18666 143 −0.24505 −0.06034 144 −0.21471 0.478091 145 0.062021 0.245054 146 0.128703 0.251266 147 −0.08979 0.120986 148 −0.01686 −0.11908 149 0.093827 0.553642 150 −0.03957 −0.55645 151 −0.29266 −0.16066 152 0.390273 0.293393 153 −0.2161 0.300892 154 0.700162 −0.04379 155 0.657845 0.460867 156 −0.24593 −0.42937 157 −0.00383 0.355383 158 0.440665 0.768201 159 −0.15086 −0.08878 160 −0.70712 −0.87748 161 −0.42352 −0.08051 162 0.513725 −0.08209 163 −0.48877 −0.18008 164 −0.22873 0.040272 165 −0.00113 0.29397 166 0.106515 0.119573 167 0.141129 0.310612 168 0.029283 −0.07189 169 0.254885 −0.36133 170 0.146097 0.155699 171 −0.31281 −0.53023 172 −0.25084 −0.14917 173 0.141674 0.332842 174 0.037511 −0.14144 175 0.306236 0.235262 176 0.227363 0.672372 177 −0.02763 −0.74887 178 0.324277 0.347386 179 0.571938 0.283112 180 −0.33717 0.146416 181 −0.91176 −0.73728 182 −0.03258 −0.57903 183 −0.00981 0.144192 184 −0.32812 −0.17407 185 0.154753 −0.50136 186 0.563866 0.308207 187 0.382776 0.019374 188 0.439278 0.664556 189 0.219328 −0.22488 190 −0.38653 0.326004 191 0.314489 0.012771 192 −0.12701 −0.81362 193 −0.2957 −0.43017 194 0.041101 0.311955 195 0.145308 −0.28147 196 0.561174 0.110213 197 0.392436 0.634688 198 −0.18019 −0.25681 199 −0.00207 0.641755 200 0.628524 −0.05038 201 −0.35407 −0.50832 202 −1.1832 −0.64462 203 −0.50521 −0.06 204 −0.05322 0.282016 205 −0.05472 −0.36064 206 −0.34314 −0.13726 207 0.422846 0.552068 208 0.245241 0.234947 209 0.422916 0.323113 210 0.295644 0.170715 211 0.252945 −0.1877 212 0.171743 −0.07606 213 −0.39141 −0.75132 214 0.102703 −0.58376 215 0.30197 −0.05727 216 0.219068 −0.12696 217 0.16692 0.60087 218 0.518199 0.743352 219 0.151034 −0.6938 220 −0.05764 0.754374 221 0.735271 0.374059 222 −0.36743 −0.2232 223 −0.95533 −1.10203 224 −0.32752 −0.22155 225 0.353274 0.033745 226 −0.4163 0.078438 227 −0.12173 −0.25926 228 0.268961 0.499232 229 0.102849 0.422606 230 0.177013 0.707539 231 0.184536 −0.18362 232 −0.29692 0.191906 233 0.422856 0.403739 234 −0.56147 −0.3524 235 0.331275 −0.53025 236 0.208699 0.121352 237 0.321185 −0.17841 238 0.63918 0.152929 239 0.016557 0.582623 240 −0.00078 −0.32827 241 0.602267 0.241723 242 0.580199 0.182785 243 0.072041 −0.29027 244 −0.92459 −0.89049 245 0.025638 −0.35368 246 −0.01213 0.098191 247 −0.35373 −0.06859 248 −0.02719 −0.30683 249 0.530257 0.486047 250 0.334835 0.084108 251 0.445446 0.580003 252 0.178144 −0.13768 253 0.446267 −0.61053 254 0.22687 0.2438 255 −0.8244 0.007268 256 0.036487 −0.21761 257 0.210414 −0.13334 258 0.198165 0.180186 259 0.385193 0.707844 260 0.252956 0.076905 261 −0.30304 −0.19392 262 0.267532 0.49041 263 0.568239 0.146866 264 0.019128 −0.45084 265 −0.96245 −0.79859 266 −0.14419 −0.27452 267 0.319705 0.282828 268 −0.06563 −0.05245 269 0.0002 −0.32114 270 0.228603 0.338158 271 0.398017 0.471874 272 0.675209 0.24046 273 −0.17874 0.000091 274 0.08205 −0.33205 275 0.528481 0.345893 276 −0.36679 −0.61998 277 −0.03875 0.045072 278 0.26725 −0.40661 279 0.684031 −0.00746 280 0.444083 0.565414 281 0.168172 −0.02131 282 −0.46121 −0.06202 283 −0.16477 0.680022 284 0.217985 0.367969 285 0.215731 −0.35663 286 −1.16002 −0.49627 287 −0.20349 −0.15535 288 −0.04902 0.141569 289 −0.12404 0.212393 290 −0.275 −0.25014 291 0.152998 0.248768 292 0.240205 0.226874 293 0.411988 0.297382 294 −0.22425 −0.1374 295 −0.31402 0.152802 296 0.288638 0.443179 297 −0.32416 −0.91627 298 0.08197 −0.24439 299 −0.17465 −0.43857 300 0.718813 0.073667 301 0.549763 0.835362 302 0.038374 −0.08445 303 −0.04175 −0.35171 304 0.405471 −0.08403 305 −0.31725 0.123633 306 −0.12411 0.073884 307 −0.87963 −0.58426 308 −0.50685 0.138949 309 0.408485 −0.27883 310 −0.16015 0.019151 311 −0.62211 0.12792 312 0.20478 −0.09979 313 0.304819 0.075326 314 0.284068 0.028721 315 −0.08562 0.2851 316 0.116882 −0.04446 317 0.670848 0.138119 318 −0.35138 −0.47389 319 −0.04829 −0.17167 320 −0.62068 −0.0673 321 0.164085 0.400686 322 0.679365 0.631526 323 −0.20465 0.222757 324 −0.05834 −0.14604 325 0.259994 −0.11419 326 0.140722 0.405258 327 −0.09553 0.087806 328 −0.89708 −0.41049 329 −0.05374 −0.17161 330 −0.23111 0.410405 331 0.052623 −0.05698 332 −0.43436 0.116803 333 0.176257 −0.12436 334 0.255225 −0.10801 335 0.209227 0.160554 336 0.152583 0.140399 337 0.108238 −0.20629 338 0.489354 0.080487 339 −0.38701 −0.2711 340 −0.57375 0.14515 341 −0.35949 −0.24821 342 0.404413 0.042078 343 0.83004 0.973249 344 −0.22586 −0.18182 345 −0.10795 −0.18211 346 0.326448 −0.21616 347 0.037056 0.188999 348 0.207069 −0.43474 349 −0.79309 −0.41817 350 −0.10995 −0.13448 351 −0.13583 0.196779 352 −0.09454 0.249088 353 0.114098 −0.51201 354 −0.06277 −0.0066 355 0.030739 0.104943 356 0.089245 0.506509 357 0.13851 −0.16745 358 0.346465 −0.05318 359 0.305717 0.390758 360 −0.57124 −0.07996 361 −0.14735 −0.08012 362 0.316356 −0.70561 363 0.234631 −0.02486 364 0.808535 1.168878 365 −0.00351 −0.31577 366 0.088283 −0.05286 367 0.040512 0.063009 368 −0.30793 0.464784 369 −0.1417 0.25236 370 −0.78908 −0.10603 371 −0.09926 −0.15619 372 −0.11163 0.245076 373 −0.17555 0.33526 374 0.194532 −0.35185 375 0.072285 −0.21255 376 0.1249 −0.04503 377 0.073888 0.058349 378 −0.01345 0.065294 379 0.170292 −0.18619 380 0.166905 0.421758 381 −0.0171 −0.58313 382 −0.33802 −0.02872 383 −0.26185 0.126446 384 −0.1691 0.345999 385 1.230522 0.848091 386 −0.49941 0.114222 387 −0.26152 −0.08266 388 0.475755 −0.56818 389 0.501029 0.063689 390 0.017664 −0.08095 391 −0.56184 −0.16015 392 −0.44203 −0.23736 393 0.081059 0.277815 394 −0.02677 0.32758 395 0.18334 −0.15914 396 0.197635 −0.09194 397 0.253548 −0.09238 398 0.228668 0.041099 399 −0.23404 −0.28024 Group 4 v(j) 0 2.880628 1 −5.78703 2 −5.35282

TABLE E 1 2 Group 5 w(i, j) 0 1.633116 −0.01787 1 −0.62108 −0.20829 2 1.913093 −0.01412 3 −1.96856 0.80515 4 0.133583 0.027592 5 0.469761 0.156819 6 0.71116 0.743258 7 0.812836 0.046079 8 −0.88466 0.708408 9 −1.90587 0.02119 10 1.066909 −0.36633 11 0.576728 0.349386 12 0.576573 −0.62547 13 −2.29197 0.687983 14 0.238057 −1.24159 15 0.457516 0.286093 16 −0.26544 −1.71114 17 0.296042 −0.70806 18 −0.18413 0.80496 19 0.952597 −0.72077 20 −0.22207 1.208819 21 −0.2052 −0.13841 22 −0.07908 −0.49014 23 1.947971 0.716275 24 0.446668 −1.57593 25 −0.15773 0.020541 26 −0.68954 0.802026 27 1.51186 −0.62119 28 1.090407 0.719696 29 −1.20834 1.642169 30 −2.14508 0.957761 31 0.396216 −0.04474 32 0.551327 1.113978 33 0.31785 −1.1189 34 −0.7388 −1.05682 35 −0.82589 0.104796 36 −0.01086 0.449585 37 −1.00865 −1.37757 38 −0.05227 0.105677 39 0.132099 0.263383 40 0.402687 −0.75319 41 0.760481 0.752159 42 0.208942 0.186062 43 0.875639 −1.09463 44 1.836774 −1.92769 45 −0.66355 0.157748 46 0.569171 0.187531 47 −0.97359 0.217252 48 1.298208 0.193359 49 1.833575 −0.09301 50 −0.04765 0.930874 51 −1.29108 −0.28887 52 0.741605 0.83145 53 1.617258 0.665168 54 0.509606 −0.34202 55 −0.52289 −1.16473 56 −1.65447 0.702827 57 −0.52738 1.006644 58 −0.47908 −1.474 59 −1.24247 0.674448 60 0.212803 0.261198 61 0.23612 −0.85479 62 −0.4217 0.729907 63 0.151497 −0.15399 64 −0.2407 0.802181 65 −0.05103 0.173889 66 −0.02474 −1.09451 67 0.74556 −0.99378 68 −1.02571 0.591872 69 0.150945 0.832713 70 0.745685 0.907195 71 1.841285 −0.10294 72 −1.4037 −0.17811 73 1.247343 −0.68575 74 0.363718 2.242145 75 −0.3419 0.164293 76 −1.98196 −0.13119 77 −0.30677 −0.47691 78 −0.50804 1.467378 79 −0.16275 −2.2218 80 −0.84948 −0.70157 81 −0.661 1.245141 82 1.271082 −1.24958 83 1.750265 −0.56693 84 0.202354 0.211588 85 0.647557 −0.95091 86 1.874839 −0.47279 87 0.526894 −1.59479 88 −0.3158 0.545521 89 −0.6846 −0.36199 90 1.142325 0.379102 91 −0.02355 2.276324 92 0.66365 0.797738 93 −2.67646 0.567422 94 0.400623 −0.49895 95 2.054157 −0.77646 96 −0.13674 0.080102 97 −1.36038 −1.48188 98 0.122525 −0.16783 99 −0.0449 1.166012 100 −0.28944 −0.63102 101 −1.24365 1.511372 102 0.537764 −0.80321 103 −0.04347 1.270253 104 0.922993 −0.30641 105 0.156597 0.134695 106 −0.15585 0.407672 107 0.998183 0.457523 108 −1.51947 0.685985 109 0.742291 −1.48412 110 −1.08993 −0.70698 111 −0.81266 2.116249 112 0.90585 0.080458 113 1.54171 0.931925 114 −0.2484 −2.08013 115 −0.25322 0.127254 116 1.237261 0.442228 117 0.030239 −0.78845 118 −2.21477 −0.41647 119 −1.41758 1.112989 120 2.362344 −1.32122 121 −0.05788 −0.25831 122 −0.11173 −0.19132 123 −0.00859 0.318572 124 1.48446 −0.01536 125 0.404989 −0.01714 126 0.188271 0.126396 127 0.459736 −0.18947 128 0.854089 0.193115 129 −0.45512 −0.22194 130 1.081616 −1.41959 131 −0.65735 −0.02727 132 1.540419 −0.16958 133 0.859011 1.064669 134 0.499077 0.496344 135 −0.70174 0.232365 136 −0.04475 0.124903 137 0.677028 1.069718 138 −0.49249 0.137786 139 −3.05996 −0.45445 140 −0.49001 −0.84128 141 0.187077 1.204593 142 0.648683 −0.62179 143 −0.4145 0.175266 144 0.839112 −0.09491 145 0.892383 −1.48356 146 −0.23322 0.904961 147 0.027881 0.287417 148 0.342177 −1.37657 149 0.226559 0.137022 150 −1.93716 0.36371 151 −0.48932 −0.31886 152 0.498358 −0.67656 153 0.738419 0.864068 154 1.248411 1.185542 155 0.716607 0.811932 156 0.093749 −2.65489 157 0.024369 1.119003 158 2.087017 0.536435 159 0.445107 −0.7034 160 −2.35185 −1.04278 161 −1.02991 −0.06381 162 1.155033 −0.79636 163 −1.37801 0.649245 164 −0.15361 −0.25945 165 −0.24387 0.184499 166 0.476368 0.72066 167 −0.06049 1.422042 168 0.289742 −0.22153 169 1.011297 −1.65898 170 0.007675 0.054371 171 −0.11519 −2.14812 172 0.667691 −0.68922 173 0.90545 −0.10237 174 0.048318 −0.1431 175 0.763572 −1.00072 176 1.972264 1.59214 177 −1.79713 0.918227 178 −0.09704 1.490765 179 0.848521 1.400365 180 −0.95535 0.91044 181 −3.94267 0.300783 182 0.333388 −1.05365 183 0.106396 −0.10122 184 −0.72442 −0.11626 185 1.139524 −2.60956 186 0.182929 2.023504 187 −0.00534 −0.43591 188 0.788548 1.763997 189 −0.11575 −0.13344 190 −0.70834 0.929717 191 0.696337 0.015223 192 −2.07644 0.245698 193 −0.83276 −0.01836 194 0.776188 0.464094 195 −0.09738 0.169003 196 0.891282 0.466628 197 1.50897 −0.24904 198 0.03632 −0.08794 199 1.513318 −0.92179 200 1.131784 0.743998 201 −0.54813 −0.69265 202 −3.20059 −1.15822 203 −0.42477 −0.15737 204 0.367595 0.252744 205 −1.17282 −0.95093 206 −1.30467 −0.59389 207 1.671015 −0.41244 208 1.813753 0.846436 209 0.863894 0.20288 210 −0.0082 0.035545 211 0.306919 −0.13532 212 0.118673 0.748655 213 −2.11774 0.737975 214 0.775423 −1.47389 215 0.709271 −0.49501 216 0.146263 −0.16975 217 1.567843 0.006499 218 2.11808 −0.5554 219 −0.06215 −0.86154 220 −0.32676 1.85614 221 1.058951 −0.12573 222 −0.98641 −0.94748 223 −2.55545 −2.30878 224 −0.04588 −1.36072 225 −0.39746 1.483424 226 −1.19669 0.43933 227 −1.37894 0.597146 228 0.929822 1.003409 229 0.330506 0.293568 230 2.281329 1.664459 231 −0.08808 −0.17784 232 0.747359 −0.25745 233 0.319927 1.155909 234 −1.18401 −0.98042 235 0.333317 0.343803 236 0.21802 −0.92137 237 1.066362 −0.69973 238 2.387336 −0.16661 239 0.975425 0.050598 240 −1.11853 1.241668 241 0.475428 0.624026 242 0.38673 −0.26307 243 −2.05334 0.526326 244 −1.5451 −3.22796 245 −1.22025 0.680508 246 0.512797 0.376656 247 −0.56901 −0.64517 248 −0.25595 −0.45231 249 0.066816 1.410666 250 1.020443 0.903051 251 1.584772 1.419337 252 0.295863 0.125109 253 0.294461 −0.50519 254 1.750022 0.092489 255 −0.871 −0.47788 256 0.007856 0.668028 257 −0.81328 −0.31354 258 0.747123 −0.32865 259 −0.31632 1.739569 260 0.825831 −0.36991 261 −0.50468 −0.02081 262 0.387979 0.584358 263 2.049293 0.13737 264 −0.482 −0.91783 265 −2.81911 −1.86775 266 −0.19503 −0.47003 267 −0.02671 1.415572 268 −0.38073 −0.70344 269 −1.4107 0.214772 270 1.253706 −1.22195 271 1.879221 0.772873 272 0.455635 0.833817 273 −0.17495 0.112013 274 −0.7729 0.539989 275 0.590563 1.456178 276 −1.18563 −0.69358 277 0.380529 0.139288 278 0.463008 −2.35149 279 0.047245 1.532602 280 2.095466 1.328176 281 −0.74064 0.522017 282 −1.07015 0.326975 283 1.914589 −1.44314 284 0.133123 1.229839 285 −0.70828 −0.26286 286 −1.60192 −1.50848 287 0.131394 −1.63553 288 0.448256 0.917572 289 0.291321 −0.70406 290 −1.77845 0.461537 291 0.801541 −0.34689 292 0.655769 0.720574 293 1.317247 −0.91426 294 0.261885 −0.25623 295 0.263911 −1.02605 296 0.551645 −0.11998 297 −0.94442 −1.69194 298 −1.12475 1.437829 299 −0.43916 −0.96252 300 1.16488 0.471043 301 2.832753 1.553714 302 0.736882 −1.83349 303 0.612951 −1.67105 304 0.454548 −0.40769 305 0.284457 0.576541 306 −0.86674 1.215636 307 −1.85671 −1.11827 308 −1.42227 1.3999 309 0.145514 1.420671 310 −0.09195 −0.2457 311 0.113107 −0.59437 312 0.644385 0.318136 313 −1.42941 1.89067 314 0.332982 0.671281 315 0.211443 0.0099 316 0.1645 −0.63417 317 2.226396 0.745519 318 −1.3663 0.554042 319 −0.62514 0.776205 320 −0.42821 −0.10153 321 −0.96343 2.018122 322 2.592806 −0.40131 323 −0.51963 −0.89171 324 0.080479 0.257162 325 0.125237 −0.36136 326 −0.09777 0.463747 327 1.339665 −1.16691 328 −2.19904 −0.1217 329 0.116225 −0.5574 330 0.370282 −0.55109 331 −0.56585 0.575709 332 0.078517 −1.25867 333 −0.63998 0.139579 334 0.878082 −0.32057 335 0.723166 0.771149 336 −0.26075 0.280087 337 0.847563 −0.94227 338 1.261161 0.568843 339 0.617729 −1.67872 340 −0.02624 −0.32565 341 −0.12063 −0.5062 342 1.413222 1.316965 343 1.767599 1.794284 344 −2.13529 1.665581 345 0.53001 −0.56849 346 0.650829 −0.85844 347 −1.99032 1.966636 348 0.619084 −1.25124 349 −1.44217 −1.70657 350 −0.31124 0.920554 351 0.764848 −0.49393 352 0.044589 0.703631 353 0.211831 −1.07207 354 −1.00136 1.054915 355 1.173388 −0.26242 356 0.741422 0.03033 357 −0.09607 0.22436 358 −0.74147 1.634693 359 −0.11593 2.330206 360 −0.17286 0.041886 361 0.00867 −0.38863 362 0.088977 −0.68523 363 0.998564 −0.79101 364 3.295628 2.146997 365 −0.75167 −0.21617 366 −1.60686 0.913739 367 −0.66005 0.546999 368 −0.56738 −0.43853 369 0.114157 −1.19931 370 −2.02121 −0.52243 371 −0.04816 −0.56476 372 0.051841 0.325243 373 −0.08187 0.030018 374 −0.35163 −0.90398 375 1.225754 −2.09676 376 1.128187 −0.05179 377 1.518524 −0.30576 378 −0.08343 −0.24672 379 0.804333 −1.01293 380 1.121503 0.944903 381 −1.25018 −0.9489 382 −1.05705 0.429744 383 0.24272 0.560046 384 0.477673 −0.07328 385 2.923389 1.499489 386 −1.47505 0.75497 387 −0.9743 0.229118 388 0.087532 −0.46502 389 1.594751 −0.82819 390 −0.91633 0.077167 391 −1.4445 −0.53334 392 0.025976 −0.66656 393 1.32135 −0.40929 394 0.78529 −0.20118 395 −0.25673 0.420163 396 −0.56328 0.202355 397 −0.67384 0.439696 398 0.664373 −0.7367 399 −0.04978 −0.01886 Group 5 v(j) 0 9.196142 1 −18.677 2 −17.1693

TABLE F Group 6 w(i, j) 1 2 0 0.194156 1.117991 1 0.306196 0.100681 2 −0.47255 0.753175 3 0.460214 −0.3743 4 0.238559 0.080866 5 0.046563 −0.04587 6 1.566442 0.954563 7 0.07199 0.707386 8 −0.1494 −0.43928 9 −0.53006 −0.77116 10 −0.92783 −0.17555 11 −0.9402 0.278499 12 0.538427 −0.04737 13 0.916818 −0.20708 14 0.302941 0.370203 15 −0.51026 −0.54404 16 0.632778 −0.33449 17 0.160891 0.109297 18 −0.06045 0.131993 19 −0.29608 0.46544 20 0.09156 0.171164 21 0.26479 −0.18186 22 0.295242 −0.11758 23 −0.20045 0.309966 24 1.145101 0.06952 25 0.387864 0.221464 26 −0.28654 −0.25546 27 −0.05406 0.523351 28 −0.51624 0.176687 29 −0.12046 −0.09845 30 −0.66592 −1.06499 31 −0.75133 −0.03212 32 −0.6909 0.626404 33 0.904151 0.399241 34 0.602963 −0.36924 35 0.778535 0.03577 36 0.049579 0.064738 37 −0.23231 −0.86144 38 −0.68323 −0.57956 39 −0.27051 0.020019 40 −0.06391 0.439718 41 0.061354 0.54394 42 −0.18255 −0.13498 43 0.069916 −0.0911 44 −0.02474 0.160674 45 1.679013 0.229751 46 0.303806 0.13677 47 −0.354 −0.56518 48 −0.07273 0.386514 49 −0.94006 0.516904 50 0.304074 0.453011 51 −0.04252 −0.6166 52 −0.30275 0.144473 53 −0.77558 0.801056 54 0.756377 0.146935 55 1.485519 0.118584 56 0.400499 −0.09301 57 −0.01681 0.039944 58 −0.52424 −0.39312 59 0.274077 −0.22339 60 −0.34806 0.511291 61 −0.43141 −0.01429 62 −0.17971 0.297837 63 0.220627 0.04956 64 −0.46382 −0.2813 65 −0.21315 −0.22772 66 0.026442 −0.67272 67 −0.24171 −0.00902 68 −0.5664 −0.56557 69 −0.11854 0.57734 70 −0.81493 0.650553 71 −0.33306 0.361563 72 −0.28481 −0.796 73 0.72284 0.609702 74 0.440822 0.966438 75 0.439831 −0.12655 76 1.455586 −0.58706 77 0.345601 0.118048 78 0.559 0.118622 79 −0.09781 −0.54527 80 0.063096 −0.17473 81 −0.44589 0.208456 82 −0.3935 −0.31145 83 −0.17209 0.588347 84 −0.19994 −0.0799 85 −0.54968 −0.38284 86 0.001385 0.362302 87 0.151668 −0.26203 88 0.81917 0.205271 89 −0.28523 −0.48724 90 0.156046 0.394402 91 −0.35324 0.917073 92 0.295767 0.426376 93 0.100462 −0.6851 94 −0.40476 −0.07134 95 −0.72272 0.917887 96 0.313144 −0.07535 97 0.769463 −0.94867 98 0.440302 0.289906 99 −0.45743 0.616925 100 0.809694 −0.18199 101 −0.59608 −0.27548 102 0.418151 0.311449 103 −0.39657 0.157578 104 0.519776 0.747633 105 0.234379 −0.15676 106 0.10838 0.098072 107 0.094636 0.304693 108 −0.27682 −0.70067 109 −0.22161 −0.17798 110 −0.08362 −0.41381 111 −0.90489 −0.02461 112 −0.14007 0.753587 113 0.067155 0.873086 114 −0.3798 −0.9137 115 −0.34528 −0.14446 116 0.302602 1.380213 117 0.475417 −0.08041 118 −0.0115 −1.47395 119 0.802573 0.105337 120 0.507734 0.577517 121 0.502951 −0.23192 122 0.410814 −0.04097 123 −0.14083 0.580671 124 −0.52138 0.160964 125 −0.15629 0.29188 126 0.221238 0.067408 127 0.275036 0.277521 128 0.263347 0.029013 129 0.574798 −0.71673 130 −0.41888 −0.57592 131 0.262045 −0.45836 132 0.401984 0.668669 133 −0.10892 0.952735 134 −0.4638 0.821051 135 0.331661 −0.50844 136 −0.8706 −0.51658 137 −0.23674 0.882646 138 −0.00142 −0.2575 139 −0.96626 −2.11124 140 0.743691 −0.19472 141 0.257894 0.42233 142 0.58293 0.026978 143 0.206359 −0.06709 144 −0.16662 0.353181 145 −0.09284 0.437149 146 0.277058 0.815602 147 −0.08838 −0.16026 148 0.484274 −0.08932 149 −0.22634 −0.06259 150 0.228699 −0.79397 151 0.275624 −0.01777 152 0.639402 0.263092 153 0.85086 0.501719 154 −0.72802 0.654746 155 −0.21891 0.925049 156 −0.4144 −0.52555 157 −1.14013 −0.27539 158 0.593081 1.155064 159 0.494722 −0.6209 160 0.491912 −1.31782 161 0.234106 −0.16594 162 −0.1584 0.445577 163 0.022092 −0.62415 164 −0.41514 −0.4056 165 −0.15452 0.342273 166 −0.36069 0.259164 167 −0.39861 0.843466 168 0.10745 0.02997 169 0.084936 0.027116 170 −0.28919 −0.41487 171 0.02309 −0.65751 172 0.070271 −0.24297 173 0.119365 0.12238 174 0.381633 0.197898 175 −0.08248 1.094715 176 0.697042 1.175009 177 −0.45417 −0.6714 178 −0.6637 0.272831 179 −0.11931 1.229861 180 0.413422 −0.144 181 0.93882 −1.0964 182 0.319356 −0.14647 183 −0.04981 0.255428 184 −0.67589 −0.87611 185 −0.17151 −0.27246 186 −0.0837 0.693432 187 −0.17891 0.402725 188 −0.39186 1.056538 189 0.191266 0.285887 190 0.291749 0.268383 191 0.197149 −0.09562 192 0.749733 −0.37677 193 0.209957 −0.3717 194 0.036095 0.239149 195 0.600324 0.095875 196 0.571475 1.004306 197 0.007175 0.978237 198 0.851697 0.408007 199 −0.2945 0.440539 200 −0.47883 0.735563 201 1.121544 −0.60953 202 0.074035 −1.75131 203 0.009405 −0.34225 204 −1.00828 −0.50245 205 −0.38994 −0.80778 206 −0.47186 −0.64466 207 −0.67351 0.810684 208 −0.64898 1.039114 209 −0.40147 0.524184 210 −0.16603 −0.12304 211 −0.46264 −0.33201 212 −0.23518 −0.51054 213 0.562688 −0.8979 214 −0.51993 −0.5674 215 0.497522 0.059764 216 0.0954 0.167056 217 −0.06555 1.010594 218 −0.65261 0.504331 219 −0.19569 −0.09996 220 −0.57064 0.43556 221 0.159059 1.329996 222 0.235949 −0.56695 223 1.539303 −1.32649 224 −0.12028 −0.47678 225 0.372077 0.437686 226 0.073827 −0.3012 227 −0.75989 −0.5024 228 0.342127 0.986697 229 0.179716 1.059812 230 0.10384 1.137089 231 0.001192 0.044351 232 0.357887 −0.13903 233 0.027373 −0.01451 234 −0.51275 −1.4981 235 0.006351 0.033694 236 0.449742 0.154951 237 0.02288 −0.1086 238 0.037804 0.604354 239 0.292632 0.57913 240 0.387725 0.185053 241 −0.54959 0.142341 242 −0.07227 0.633157 243 0.653378 −0.31679 244 1.168255 −1.58462 245 −0.00585 −0.37544 246 0.029099 0.01152 247 −0.23573 −1.0051 248 −0.00706 −0.19576 249 0.272482 0.800524 250 −0.69518 1.361433 251 −0.47275 0.876853 252 −0.09466 −0.21039 253 1.153502 0.445206 254 0.00961 −0.16343 255 −0.16476 −0.84249 256 −0.48053 −0.21428 257 −0.09956 −0.24072 258 −0.88902 −0.11863 259 −0.22247 1.165445 260 −1.14911 −0.47859 261 0.391243 0.09873 262 −0.05926 0.502002 263 −0.31322 1.160954 264 0.772157 −0.42011 265 1.565001 −1.12889 266 0.215263 −0.20118 267 0.211744 0.137523 268 0.424963 −0.17271 269 0.275911 −0.04296 270 −0.50519 0.111862 271 −0.60363 1.197893 272 −0.47148 0.824977 273 0.085593 0.137813 274 0.447739 0.143006 275 −0.03992 0.115299 276 0.261498 −0.70968 277 −0.04358 0.028798 278 0.159182 −0.17423 279 −0.36734 0.296901 280 −0.42459 1.389664 281 0.116644 0.154608 282 0.861271 0.488997 283 −0.14748 0.437403 284 −0.05037 0.507787 285 0.146532 0.097587 286 0.124344 −1.85601 287 −0.26116 −0.46528 288 −0.6275 −0.47282 289 0.259101 0.04512 290 0.450497 −0.22489 291 −0.36566 0.036476 292 −0.00526 0.189985 293 0.350931 0.555475 294 0.079836 0.075694 295 −0.11523 −0.05845 296 0.266857 0.419854 297 −0.48928 −1.17017 298 −0.06078 0.126367 299 −0.18135 −0.37674 300 −0.03226 0.882241 301 −0.48327 1.880237 302 −0.60118 −0.41571 303 −0.60353 0.050797 304 0.237347 0.352758 305 0.433406 0.347242 306 0.4569 −0.01268 307 −0.2108 −1.4921 308 0.100106 0.418934 309 0.320633 0.528209 310 0.51772 0.194672 311 0.524128 −0.10414 312 −0.47661 0.298452 313 −0.22204 0.220658 314 0.394238 0.594652 315 −0.00582 −0.19766 316 −0.44098 0.006551 317 −0.19014 0.086582 318 1.02593 0.034311 319 −0.30411 0.002061 320 −0.12958 −0.58703 321 0.730547 1.050286 322 −0.21381 1.36341 323 0.009169 −0.17716 324 0.453818 0.339903 325 −0.09685 0.193984 326 −0.45404 0.177061 327 0.122101 −0.18815 328 0.701163 −0.81285 329 −0.55634 −0.52228 330 −0.0955 0.176016 331 −0.68134 −0.12819 332 0.04524 −0.12684 333 0.22143 0.232142 334 −0.4976 0.06614 335 0.397612 0.402411 336 −0.22483 −0.08715 337 −0.13806 0.154218 338 −0.48828 0.21819 339 0.032894 −0.57715 340 0.496065 0.424603 341 0.293301 −0.17337 342 0.263856 0.704202 343 −0.78979 1.671367 344 −0.9776 −0.44254 345 −0.19344 −0.22385 346 −0.03965 0.019001 347 0.099459 0.654128 348 −0.2879 −0.26845 349 0.496068 −0.87151 350 0.106283 −0.25608 351 0.620182 0.285442 352 0.43397 0.133584 353 −0.12667 −0.31941 354 0.249208 0.160281 355 −0.40872 0.35512 356 0.020685 0.618508 357 0.268405 0.018641 358 0.012056 0.157036 359 −0.05556 0.381074 360 0.462051 0.33664 361 −0.02219 0.293858 362 0.861292 0.239672 363 −0.41859 −0.04352 364 −0.31008 2.180656 365 0.104728 −0.20392 366 0.153536 −0.03619 367 −0.23049 −0.01205 368 0.004354 0.303282 369 0.123926 −0.45284 370 0.523208 −0.81964 371 0.233119 −0.03303 372 −0.01624 −0.03783 373 −0.08075 −0.1685 374 −0.67335 −0.49152 375 0.141293 −0.22266 376 −0.26699 0.011106 377 −0.05159 0.189023 378 −0.12348 0.196946 379 −0.02404 −0.00173 380 −0.39094 0.646177 381 −0.4762 −0.43927 382 0.091719 −0.2174 383 −0.64943 −0.21649 384 −0.34292 −0.20055 385 −0.97846 2.133044 386 0.693497 0.234331 387 0.370507 −0.35427 388 0.034654 −0.22827 389 0.026766 0.290931 390 0.069503 −0.41583 391 0.097578 −1.11522 392 0.401505 0.1393 393 0.563007 0.440274 394 −0.34986 −0.29784 395 −0.25839 −0.44839 396 0.587678 0.181805 397 0.228767 0.545136 398 −0.30482 0.311115 399 0.045441 −0.11562 Group 6 v(j) 0 −1.41045 1 6.940413 2 −10.4233

TABLE G 1 2 Group 7 w(i, j) 0 −0.16116 0.952026 1 −0.32202 0.025618 2 0.577338 2.091769 3 0.547314 −0.82647 4 −0.21961 −0.11748 5 0.259493 0.01009 6 0.037505 0.557986 7 0.984537 0.451684 8 1.179184 −1.06802 9 0.134425 −0.68651 10 −0.47375 0.523121 11 0.297758 0.151143 12 −0.6666 0.452625 13 −0.9244 −0.14154 14 −0.76154 0.447989 15 0.19593 −0.54365 16 −1.20564 −0.08764 17 0.559777 −0.5726 18 −0.28401 0.204275 19 0.282494 0.592133 20 0.223333 0.136176 21 0.172376 0.045282 22 −1.67958 0.501968 23 1.004569 0.640574 24 −1.74296 0.69751 25 −0.27663 0.290629 26 −0.01177 −0.3867 27 0.047008 0.595556 28 0.173677 0.759059 29 0.369319 −0.39987 30 0.523654 −0.7363 31 0.737732 −0.03419 32 0.207484 0.360778 33 −0.11674 0.099155 34 −0.9762 −0.34034 35 −0.33133 −0.12398 36 0.962934 −0.52256 37 −0.20453 −0.66836 38 −0.66838 0.169429 39 1.027828 −0.65309 40 0.31039 0.058132 41 0.316571 0.206955 42 0.016275 −0.21301 43 −0.33655 0.362337 44 −0.31345 0.798333 45 −0.90054 −0.08791 46 0.288776 0.20399 47 −0.09455 −0.13539 48 0.51467 0.210544 49 0.230771 0.86127 50 −0.6495 0.225224 51 0.158882 −0.66128 52 −0.25408 0.905009 53 1.208907 0.639759 54 0.218249 −0.26201 55 −0.68484 −0.19948 56 0.225061 −0.63116 57 0.491608 −0.46188 58 0.014772 −0.26975 59 −0.11951 −0.33449 60 0.077088 0.733437 61 0.641571 −0.05755 62 0.351657 0.337222 63 0.008663 0.234405 64 −0.28145 0.194142 65 −0.2022 1.109594 66 −0.21643 −0.25816 67 −0.0611 0.252675 68 −0.336 −0.30978 69 0.891509 0.367366 70 0.480627 1.348569 71 −0.72904 0.687807 72 −0.07202 −1.21576 73 −1.38784 0.794157 74 0.030905 0.545277 75 −0.36854 −0.08744 76 −0.43898 −1.07104 77 0.072127 −0.29637 78 0.038991 −0.3736 79 0.066868 −0.87201 80 −0.6034 0.262139 81 1.143917 −0.91287 82 0.318877 −0.11209 83 0.290785 0.334883 84 −0.24084 −0.16428 85 0.793954 −0.72614 86 0.0681 0.532904 87 0.055778 −0.47404 88 −0.65457 0.714498 89 −0.12146 0.218392 90 0.880572 0.050742 91 1.178395 0.301675 92 −0.01813 0.75307 93 0.219745 −0.9708 94 −1.00945 0.671983 95 0.576366 0.399846 96 0.381798 −0.23557 97 −0.62553 −0.87244 98 0.568739 −0.93272 99 0.287672 0.645434 100 −0.84269 −0.00767 101 0.548424 −0.31304 102 −0.61381 0.363308 103 −0.24645 0.30292 104 −0.41172 0.513523 105 −0.27476 −0.19388 106 0.209509 0.048639 107 0.28158 0.136281 108 0.068161 −0.97228 109 0.155841 0.0172 110 0.00633 −0.40658 111 0.907108 −0.17721 112 −0.11386 0.775573 113 0.444104 0.605973 114 −0.00253 −1.08272 115 −0.47473 −0.07385 116 0.492717 0.878332 117 −0.30503 −0.07812 118 −1.08111 −0.96659 119 0.185648 −0.13622 120 −0.37399 0.99358 121 −0.0055 −0.79363 122 −0.96044 0.333197 123 −0.03455 −0.0014 124 −0.12856 0.451339 125 0.247729 0.081733 126 0.263341 0.271675 127 0.246978 −0.21531 128 0.005498 0.117313 129 −0.41252 −0.49146 130 0.226321 −0.54646 131 −0.46116 0.097586 132 0.92645 −0.14832 133 0.723156 1.507419 134 0.697545 0.33707 135 −0.53302 −0.44478 136 −0.14883 0.013437 137 0.710592 0.679529 138 0.233794 −0.78629 139 −1.41571 −1.15975 140 −0.61608 −0.31949 141 0.34281 0.363431 142 −0.30402 −0.41221 143 −0.21014 −0.08596 144 0.37367 −0.26087 145 −0.16392 0.854498 146 −0.28934 0.656717 147 −0.22147 −0.09179 148 0.050573 −0.35 149 −0.12584 0.408706 150 −0.34467 −0.61728 151 0.500646 −0.47403 152 −0.25914 −0.27107 153 0.746127 −0.33074 154 1.44325 0.908748 155 −0.29912 1.122012 156 −0.37679 −0.534 157 0.320957 −0.27257 158 −0.2564 0.639578 159 0.627944 −1.11724 160 −1.68237 −0.9094 161 −0.66335 0.123786 162 0.556378 0.256135 163 −0.27528 −0.79806 164 −1.11223 0.831075 165 −0.42788 0.391855 166 0.779897 −0.11279 167 0.683911 0.799801 168 −0.02281 −0.20089 169 −0.43741 0.182329 170 0.118584 0.104221 171 −0.45789 −0.36884 172 −0.25323 0.284032 173 0.480395 0.030552 174 0.571073 −0.40809 175 0.5511 0.627068 176 0.494763 0.466723 177 −0.14581 −0.16282 178 0.119332 0.33166 179 0.263196 0.827155 180 −0.72626 −0.18538 181 −0.16067 −1.81726 182 −0.47213 −0.31826 183 0.173686 −0.25636 184 −0.1471 −0.73623 185 −0.83421 0.269216 186 −0.08911 0.699163 187 0.729552 −0.36486 188 0.511894 0.938879 189 0.024353 0.098312 190 0.09891 −0.18622 191 0.028666 0.360353 192 0.150558 −0.99021 193 −0.01256 −0.18229 194 0.206479 0.011154 195 0.347881 −0.03464 196 0.46512 0.608844 197 −0.63944 1.131016 198 −0.5466 0.471751 199 −0.50893 0.775994 200 0.410304 0.794308 201 −0.30276 −0.9032 202 −0.70618 −1.92498 203 0.263135 −0.48577 204 0.259449 −0.31257 205 0.041894 −0.71755 206 −0.67119 −0.00392 207 0.71847 0.273196 208 1.152892 0.29791 209 −0.35021 1.304214 210 −0.28575 −0.03429 211 0.006433 −0.32892 212 0.392356 −0.51691 213 0.836076 −2.1572 214 −0.26051 0.351812 215 0.458575 −0.2674 216 0.004712 0.241106 217 −0.67989 1.429458 218 0.696202 0.531781 219 −0.49787 0.254954 220 0.921626 0.209449 221 −0.15413 0.723596 222 −0.28136 −0.66827 223 −1.37797 −1.65337 224 −0.2317 −0.47489 225 −0.05378 0.00638 226 −0.20323 −0.20444 227 −0.7349 0.215366 228 0.222201 0.719393 229 −0.11264 1.197522 230 0.073209 1.618749 231 −0.08599 −0.00337 232 −0.42299 0.211071 233 0.473687 −0.36608 234 −0.40803 −0.80058 235 0.447448 0.107415 236 −0.21912 −0.26223 237 0.145861 0.584819 238 0.052241 0.841711 239 −0.21356 0.615208 240 0.184003 −0.35891 241 1.012649 −0.0815 242 −0.1204 0.719037 243 −0.31649 −0.65588 244 −1.75328 −0.93674 245 −0.12473 −0.44169 246 0.001966 0.086703 247 0.202073 −0.85561 248 0.066234 −0.28649 249 0.110118 0.129543 250 0.130556 1.557635 251 0.039979 0.869844 252 0.226513 −0.16183 253 −0.23691 −0.01831 254 −0.11286 0.295167 255 −0.70859 −0.21826 256 0.337634 0.272778 257 0.328478 −0.94128 258 1.119938 −0.22344 259 0.73273 1.161907 260 −0.17326 0.683648 261 0.473915 −0.3837 262 0.870057 0.079204 263 0.19465 0.798324 264 −0.9505 0.136983 265 −1.87403 −0.88188 266 −0.33104 −0.40796 267 0.492426 −0.35027 268 −0.26282 −0.23165 269 0.276232 −0.39329 270 0.918487 −0.232 271 0.628287 1.132801 272 −0.71454 1.243445 273 −0.18391 −0.09509 274 0.154282 −0.29892 275 −0.5197 0.593967 276 −0.5339 −0.00346 277 −0.04428 0.304153 278 −0.05151 −0.14267 279 0.569344 0.822627 280 1.277337 0.533094 281 0.037228 0.429038 282 −0.04906 −0.12204 283 −0.36835 0.865235 284 −0.19801 0.235206 285 −0.03786 0.174635 286 −0.62758 −1.85625 287 0.064 −0.2429 288 0.492912 −0.28661 289 0.543405 −0.38539 290 −0.39653 −0.42192 291 −0.31924 0.399616 292 0.477591 0.434302 293 −0.95127 0.85898 294 0.120295 −0.01517 295 −0.09382 0.103287 296 −0.28005 0.863913 297 −0.44324 −0.62813 298 −0.084 0.454225 299 −0.07921 −0.14424 300 0.131555 0.814075 301 −0.21798 1.835027 302 0.533602 −0.73434 303 0.40985 −0.45349 304 0.106818 0.176583 305 0.084243 −0.94748 306 −0.1197 −0.23802 307 −0.77802 −1.32853 308 0.723337 −0.87406 309 0.156401 0.212868 310 −0.82775 0.731181 311 −0.09839 −0.35822 312 0.377462 −0.06259 313 −0.29508 0.686754 314 0.258617 0.059888 315 −0.27161 −0.18004 316 −0.06366 0.536997 317 0.494787 0.263148 318 −0.229 −0.28755 319 0.035704 0.294238 320 −0.00665 −0.44558 321 0.60288 0.517194 322 0.322324 1.062177 323 0.305631 −0.62619 324 −0.7877 0.712856 325 −0.48418 0.552661 326 0.51245 −0.93216 327 −0.42594 −0.0971 328 −0.99706 −0.6507 329 0.090135 0.083225 330 −0.58068 0.070852 331 0.364399 −0.17893 332 −0.02607 −0.14066 333 0.509021 −0.76237 334 −0.50758 1.123283 335 0.273302 0.230054 336 0.199687 0.276129 337 0.398315 −0.07461 338 −0.04843 0.285003 339 −0.8104 0.361751 340 −0.66519 0.609338 341 −1.8071 0.657019 342 1.072492 0.49836 343 0.945935 1.252245 344 0.463992 −0.35137 345 0.544405 −0.52372 346 0.208211 0.102906 347 0.071478 −0.56062 348 0.477881 −0.74869 349 −0.54452 −1.11115 350 −0.13797 −0.23512 351 −0.2446 −0.16621 352 −0.46765 0.371339 353 −0.29119 0.109423 354 0.937551 −1.11605 355 0.116678 0.900321 356 −0.06633 0.93897 357 0.006084 −0.04327 358 −0.14393 0.314732 359 −0.29552 0.34999 360 0.101242 −0.30007 361 −0.48111 0.627135 362 −0.53688 0.448549 363 0.513632 0.105445 364 1.068519 1.835874 365 0.524791 −0.60243 366 0.165395 −0.32997 367 −0.39774 −0.07011 368 −0.14967 −0.26553 369 −0.45352 −0.20844 370 −0.44374 −1.15758 371 0.193073 −0.03592 372 0.090713 −0.24465 373 0.103573 0.154867 374 −0.02979 0.115943 375 0.224572 −0.48044 376 −0.0975 0.889975 377 0.293523 0.357257 378 −0.0797 0.152286 379 −0.13368 0.136809 380 0.040422 0.564384 381 −0.61705 0.321536 382 0.634972 −0.71585 383 0.101148 0.111547 384 −0.02348 0.397552 385 0.91179 1.208421 386 −0.15862 −0.10794 387 −0.10705 −0.45336 388 0.047635 −0.48201 389 −0.35233 0.268381 390 −0.60686 0.001003 391 −0.03156 −1.36357 392 0.165383 −0.48752 393 −0.49348 0.412971 394 0.284205 −0.19159 395 −0.34574 0.03731 396 −0.11658 −0.15478 397 0.54125 0.570973 398 0.110871 0.145109 399 0.34038 0.103448 Group 7 v(j) 0 5.144898 1 −9.0301 2 −10.2899

TABLE H 1 2 Group 8 w(i, j) 0 0.280176 0.322336 1 0.089863 −0.16466 2 0.258712 0.13301 3 −0.35689 −0.10317 4 0.072041 −0.08645 5 −0.23186 0.270893 6 0.31259 0.16543 7 0.559172 −0.00685 8 0.06183 −0.15552 9 −0.15374 −0.21874 10 0.101713 0.085875 11 0.558737 0.326798 12 0.046735 −0.00874 13 −0.24817 −0.4984 14 −0.05777 −0.02885 15 0.206622 0.054918 16 −0.20067 −0.2843 17 −0.15782 0.154129 18 0.261983 −0.03436 19 −0.19116 0.10826 20 0.384408 −0.0457 21 −0.07824 −0.12549 22 −0.2621 0.151674 23 0.05061 0.419858 24 −0.40798 0.043756 25 0.03181 0.065562 26 −0.0728 −0.35157 27 0.18568 0.048925 28 0.258083 0.374686 29 −0.20178 0.150815 30 −0.37952 −0.13445 31 −0.07022 0.128067 32 0.487422 0.357583 33 −0.13862 −0.076 34 −0.50341 −0.2973 35 −0.16533 −0.12502 36 0.326894 −0.25499 37 −0.24026 −0.42517 38 −0.21263 −0.38549 39 0.063399 −0.03075 40 0.121922 −0.03443 41 0.321519 −0.0844 42 0.224381 −0.28818 43 0.027942 0.194588 44 0.125309 0.481723 45 −0.14902 −0.07481 46 −0.07075 0.080686 47 −0.23067 0.02413 48 0.262883 0.383931 49 0.170966 0.311139 50 −0.04542 0.210747 51 −0.26566 −0.11295 52 0.204875 0.106507 53 0.411018 0.59082 54 −0.0726 −0.09807 55 −0.44838 −0.25068 56 −0.26283 0.077592 57 0.053487 0.200935 58 −0.08799 −0.06156 59 −0.19695 −0.31923 60 0.199526 0.080912 61 −0.07185 −0.19526 62 0.196695 0.332062 63 −0.18528 0.045242 64 0.307743 −0.15154 65 0.273907 0.263797 66 −0.176 −0.15571 67 0.044056 −0.05496 68 −0.30912 −0.04222 69 0.449623 0.328544 70 0.408023 0.352031 71 0.047199 0.197917 72 −0.14097 −0.20277 73 0.121769 0.144908 74 0.457205 0.433156 75 −0.16274 −0.09385 76 −0.60701 −0.25247 77 −0.07979 −0.11969 78 −0.00318 0.257171 79 −0.1114 −0.10213 80 −0.19517 −0.20672 81 0.176544 0.049347 82 −0.10583 −0.14123 83 0.356354 0.167297 84 0.11891 0.042833 85 0.180655 −0.20791 86 0.280233 0.099587 87 −0.19843 0.12152 88 −0.13518 0.130912 89 −0.04634 −0.11816 90 0.324811 0.214844 91 0.167347 0.391105 92 0.520048 −0.06311 93 −0.3756 −0.26741 94 −0.00007 0.143016 95 0.257771 0.641781 96 −0.15785 −0.11424 97 −0.62828 −0.51594 98 −0.35792 0.070469 99 0.285154 0.138717 100 −0.24297 −0.05282 101 −0.2569 −0.09424 102 0.149283 −0.15182 103 −0.2092 0.192871 104 0.230196 0.059552 105 −0.13162 −0.00127 106 0.044484 0.028085 107 0.192866 0.09894 108 −0.233 −0.09201 109 −0.13998 0.01842 110 −0.15383 0.110923 111 0.173836 0.274321 112 0.51414 0.133339 113 0.182077 0.371687 114 −0.29869 −0.42132 115 0.053145 0.03305 116 0.352281 0.588561 117 −0.18262 −0.06152 118 −0.79579 −0.57692 119 −0.12687 −0.1593 120 0.316487 0.038593 121 0.017199 −0.17629 122 −0.09134 −0.22363 123 −0.04756 0.228905 124 0.252189 −0.09371 125 0.116935 0.12619 126 0.251119 0.050925 127 0.127259 −0.0269 128 0.05564 0.288694 129 −0.25431 −0.24257 130 −0.03116 −0.12309 131 −0.05097 0.022442 132 0.04139 0.249297 133 0.529803 0.28221 134 0.361491 0.42698 135 −0.51547 −0.00114 136 0.053323 0.010736 137 0.696979 0.243455 138 −0.04103 −0.13276 139 −0.87638 −0.56972 140 −0.29005 0.0786 141 0.394238 −0.04498 142 −0.11369 −0.22259 143 −0.32284 0.008446 144 −0.08911 0.2045 145 −0.10728 0.052944 146 0.177407 0.098888 147 −0.09009 0.120616 148 −0.07467 0.01718 149 −0.00037 0.392235 150 −0.22564 −0.21368 151 −0.05539 0.048398 152 0.221042 0.003341 153 −0.21499 0.160504 154 0.641006 0.106168 155 0.363684 0.414426 156 −0.1965 −0.29292 157 0.185528 0.232695 158 0.269708 0.635684 159 −0.17473 −0.232 160 −0.76539 −0.79342 161 −0.16027 0.078819 162 0.308538 0.108572 163 −0.29246 −0.25191 164 −0.15875 −0.10026 165 0.145114 0.27188 166 0.172042 0.061138 167 0.295894 0.293787 168 0.028913 −0.07227 169 0.026949 −0.12841 170 0.087546 0.153603 171 −0.18152 −0.34885 172 −0.0285 −0.1266 173 0.018039 0.117074 174 0.013201 −0.17427 175 0.328484 0.283735 176 0.263523 0.462784 177 −0.04506 −0.39274 178 0.21313 0.100068 179 0.639239 0.458409 180 −0.29708 −0.15314 181 −0.75986 −0.8363 182 0.140368 −0.35048 183 −0.02458 0.328242 184 −0.17431 −0.43726 185 0.000826 −0.37192 186 0.376571 0.251457 187 0.334845 −0.00291 188 0.462598 0.616313 189 0.218829 −0.22532 190 −0.12587 0.119885 191 0.276037 0.059948 192 −0.15675 −0.40897 193 −0.25608 −0.043 194 −0.01207 0.085644 195 0.003494 −0.09893 196 0.571325 0.162064 197 0.398344 0.495579 198 −0.08543 −0.22323 199 0.008196 0.408179 200 0.591552 0.060628 201 −0.49251 −0.30129 202 −1.07518 −0.71723 203 −0.29767 −0.10512 204 0.099298 0.197993 205 −0.19574 −0.24457 206 −0.37491 −0.12382 207 0.329921 0.421738 208 0.105327 −0.01787 209 0.432718 0.221158 210 0.294576 0.169892 211 0.200918 −0.17751 212 0.155954 −0.10067 213 −0.32383 −0.38157 214 0.182018 −0.27661 215 0.032786 −0.17018 216 0.222737 −0.08613 217 0.07883 0.595989 218 0.516062 0.610738 219 0.148437 −0.38454 220 0.09305 0.514056 221 0.619208 0.253326 222 −0.50617 −0.26182 223 −1.03036 −0.98533 224 −0.09114 −0.09227 225 0.430771 0.115833 226 −0.24198 −0.08795 227 −0.1943 −0.24671 228 0.256378 0.37642 229 0.097133 0.178745 230 0.291176 0.598428 231 0.185446 −0.18283 232 −0.1262 0.081021 233 0.364879 0.20601 234 −0.16759 −0.33473 235 0.354533 −0.13748 236 0.088811 0.048252 237 0.275667 0.066499 238 0.553402 0.198148 239 0.192956 0.252252 240 0.046442 −0.11814 241 0.549325 0.021857 242 0.534248 0.197887 243 −0.18942 −0.26986 244 −1.0251 −0.7881 245 0.085048 −0.29609 246 0.286335 0.242831 247 −0.35344 −0.03213 248 −0.05745 −0.3493 249 0.261177 0.485355 250 0.429397 0.036518 251 0.304101 0.37675 252 0.178639 −0.13729 253 0.146889 −0.20496 254 0.311676 0.069606 255 −0.2809 0.066729 256 0.173884 −0.00731 257 0.082149 −0.12322 258 0.131881 0.256422 259 0.436154 0.519177 260 0.19433 0.131613 261 −0.05006 −0.10751 262 0.356847 0.239002 263 0.557269 0.137655 264 −0.20516 −0.27195 265 −0.89702 −0.78432 266 −0.18417 −0.20021 267 0.330243 0.174138 268 0.065072 −0.16737 269 −0.05387 −0.20715 270 0.223589 0.123392 271 0.157142 0.260878 272 0.489482 0.289157 273 −0.17691 0.001684 274 0.079506 −0.13101 275 0.284311 0.107616 276 −0.14871 −0.3219 277 0.075672 0.086463 278 0.03304 −0.24115 279 0.451536 0.09847 280 0.393575 0.47111 281 0.215062 −0.08996 282 −0.1232 0.106244 283 0.052652 0.321821 284 0.146523 0.361367 285 −0.08415 −0.18466 286 −0.98776 −0.64694 287 −0.14207 −0.01228 288 0.22634 0.09001 289 −0.06194 0.277908 290 −0.20718 −0.25136 291 0.019461 0.093787 292 0.023885 0.067402 293 0.378495 0.283371 294 −0.22544 −0.13846 295 −0.10132 0.020483 296 0.2432 0.240385 297 −0.19961 −0.41433 298 0.104077 −0.14921 299 0.053988 −0.32661 300 0.38022 0.138622 301 0.562018 0.715657 302 −0.13685 −0.14249 303 −0.03016 −0.22117 304 0.14678 −0.04298 305 −0.10325 −0.00728 306 −0.1241 −0.11444 307 −0.76743 −0.67222 308 −0.27217 0.198293 309 0.218046 −0.1459 310 −0.04301 0.159191 311 −0.58886 −0.0227 312 0.092836 −0.1229 313 0.194934 −0.01003 314 0.244997 −0.00846 315 −0.08548 0.285201 316 −0.03473 0.141617 317 0.438175 0.051332 318 −0.16444 −0.26022 319 −0.07391 0.202322 320 −0.28044 −0.0554 321 0.114254 0.401794 322 0.492382 0.57594 323 −0.0815 −0.15213 324 −0.03754 −0.04391 325 0.157412 0.035032 326 −0.02602 0.392123 327 −0.17738 −0.14248 328 −0.59422 −0.45361 329 0.009462 −0.02529 330 −0.16892 0.339293 331 0.209446 0.089063 332 −0.24768 −0.05874 333 0.128149 −0.20183 334 0.045111 −0.16833 335 0.076539 0.080288 336 0.152465 0.140161 337 0.002925 −0.04547 338 0.344921 0.020747 339 −0.16712 −0.1798 340 −0.28057 0.172974 341 −0.28399 −0.09391 342 0.242239 0.080815 343 0.629515 0.717999 344 −0.36706 −0.14904 345 −0.18594 −0.05377 346 0.122529 −0.03742 347 0.209078 0.088422 348 0.142492 −0.3696 349 −0.49413 −0.46858 350 0.017413 −0.03532 351 0.022092 0.02744 352 0.021223 0.167044 353 −0.08818 −0.33604 354 −0.10013 −0.07328 355 −0.10447 0.035356 356 0.158499 0.269667 357 0.137598 −0.16839 358 0.053401 0.09205 359 0.295167 0.254434 360 −0.22037 0.040353 361 0.1523 0.007335 362 0.160472 −0.38438 363 0.079779 0.095844 364 0.593924 0.902876 365 −0.07806 −0.24758 366 −0.03983 −0.17643 367 −0.02031 0.142277 368 −0.06825 0.348749 369 −0.2862 0.084045 370 −0.68083 −0.2086 371 −0.05227 −0.0774 372 0.043616 0.013121 373 0.193444 0.212376 374 0.038471 −0.24379 375 0.016123 −0.24717 376 −0.04567 0.058567 377 0.179515 0.190871 378 −0.01504 0.063935 379 0.035176 0.008966 380 0.195784 0.384433 381 0.055274 −0.34632 382 −0.25716 0.151064 383 −0.09593 0.058775 384 0.019821 0.176833 385 0.901357 0.659182 386 −0.38373 −0.08401 387 −0.33863 −0.0348 388 0.247882 −0.15263 389 0.382067 −0.01182 390 0.023522 −0.09082 391 −0.45018 −0.25501 392 −0.0551 −0.19082 393 0.288189 0.113233 394 0.081899 0.318285 395 −0.04854 −0.16885 396 0.052214 −0.11094 397 0.137644 −0.2618 398 0.194715 0.197988 399 −0.23755 −0.28356 Group 8 v(j) 0 2.513683 1 −4.36612 2 −3.85445

TABLE I Group 9 w(i, j) 1 2 0 0.64194 0.270091 1 0.195859 −0.6188 2 0.534558 0.496142 3 −0.87565 0.061475 4 −0.06192 0.345997 5 −1.18645 0.933661 6 0.467275 0.126926 7 0.984155 −0.39572 8 0.151643 −0.12714 9 0.320599 −0.7048 10 0.52666 −0.06082 11 1.089887 0.035408 12 −0.0923 0.225278 13 −0.72464 −0.25572 14 −0.86248 0.050058 15 0.147439 0.053642 16 −0.29571 −0.51335 17 −0.15325 0.069256 18 0.953717 −0.46928 19 −0.24658 0.612544 20 0.803891 −0.25394 21 −0.0769 −0.12496 22 −0.14417 −0.63508 23 0.576635 0.957538 24 −0.74671 −0.28942 25 0.429834 −0.13955 26 −0.24778 −0.4306 27 0.581436 −0.0015 28 0.721117 0.116565 29 −0.66842 0.77073 30 −0.85377 0.434075 31 0.054877 0.509492 32 0.441406 0.826331 33 0.112802 −0.07728 34 −1.08547 −0.48129 35 −0.26093 −0.46607 36 −0.04708 −0.29622 37 −1.11634 0.063518 38 −0.03217 −0.69024 39 0.560496 −0.14397 40 0.103567 0.052875 41 1.17473 −0.59104 42 0.224769 −0.28789 43 0.014872 −0.11585 44 0.35228 1.081893 45 −0.31757 −0.11967 46 0.121239 −0.07055 47 −0.8264 −0.08918 48 0.097376 0.713038 49 0.623651 1.05684 50 −0.34583 0.247849 51 −0.91097 0.395358 52 0.63771 −0.10862 53 0.657779 1.129134 54 −0.0481 −0.50822 55 −0.81004 −0.25981 56 −0.58872 0.189189 57 −0.20744 −0.27762 58 −0.19968 −0.09627 59 0.426767 −0.89817 60 0.653613 −0.39879 61 0.028338 −0.21747 62 0.752471 0.257402 63 −0.1843 0.04568 64 0.277822 −0.74439 65 0.692065 0.601465 66 −0.15557 −0.34936 67 −0.12144 0.157933 68 −0.6335 0.165339 69 0.858233 0.331915 70 0.226071 0.656136 71 0.199787 −0.34098 72 −0.63458 −0.5201 73 −0.36468 0.620908 74 0.259614 1.166547 75 0.117573 −0.25142 76 −1.15267 −0.0683 77 0.26628 −0.79707 78 0.382105 −0.55314 79 −0.38318 −0.21845 80 0.234626 −0.32187 81 −0.12815 0.031953 82 0.259737 0.082435 83 0.910008 0.966931 84 0.121696 0.044944 85 0.275588 −0.74298 86 0.458071 −0.35126 87 −0.49655 0.00218 88 −0.11105 −0.06496 89 −0.2502 0.079157 90 0.523925 −0.23767 91 0.229805 1.023343 92 1.035111 −0.08909 93 −0.68921 −0.11272 94 −0.17698 0.102316 95 0.33117 1.367461 96 0.140862 0.098976 97 −1.15189 −0.96311 98 −0.77562 0.398092 99 0.847465 −0.07587 100 −0.61258 −0.04538 101 0.074122 −0.18041 102 −0.2131 0.164791 103 0.286545 0.424462 104 0.42088 −0.23242 105 −0.12945 0.000264 106 −0.11031 −0.1573 107 0.382466 −0.39352 108 −0.51306 −0.06702 109 −0.02756 −0.09547 110 −0.50884 0.212841 111 −0.07683 0.819798 112 0.354268 0.353191 113 0.27911 −0.14657 114 −0.6447 −0.28158 115 0.306664 −0.28371 116 1.089572 0.766528 117 −0.08145 0.182469 118 −1.2225 −0.68656 119 −0.1273 −0.18348 120 0.969078 −0.4354 121 −0.05033 −0.37569 122 0.216231 −0.61049 123 −0.70487 0.544751 124 0.770164 0.46746 125 0.207107 0.563171 126 0.251933 0.051569 127 −0.14306 0.095492 128 0.53051 0.370838 129 −0.8089 0.238253 130 0.199101 −0.44365 131 −0.85422 0.441722 132 0.462494 0.007296 133 0.599888 0.389471 134 0.526516 0.564856 135 −1.37953 0.51871 136 0.298681 −0.4019 137 1.694115 0.157266 138 0.206048 0.47354 139 −1.39902 −0.87779 140 −0.69132 0.08969 141 0.857214 −0.62908 142 −0.15679 −0.69497 143 −0.07203 −0.27461 144 −0.91135 1.145603 145 0.727183 −0.01054 146 0.418721 0.336123 147 −0.08732 0.122543 148 −0.898 0.331623 149 0.053974 0.560811 150 0.050149 −0.25342 151 0.458407 −0.4585 152 −0.14336 0.15496 153 −0.11636 0.192769 154 0.555904 0.376013 155 0.182186 0.965759 156 −0.09942 −0.38636 157 0.028325 0.143316 158 0.871104 1.423339 159 −0.06471 −0.34219 160 −1.03126 −1.19913 161 −0.16424 −0.12197 162 0.746217 −0.0971 163 −0.66526 −0.32622 164 −0.22201 −0.30147 165 0.563351 0.033633 166 −0.06711 0.145258 167 0.605177 0.045812 168 0.030987 −0.07084 169 −0.12778 0.075078 170 −0.15755 −0.20566 171 0.342908 −0.42727 172 0.200543 −0.64354 173 −0.43139 0.161183 174 −0.13837 −0.11641 175 0.057848 −0.08861 176 −0.02743 0.755987 177 0.315783 −0.46494 178 0.056731 0.794653 179 1.011103 0.159911 180 −0.26479 0.312825 181 −1.75305 −0.00027 182 0.241128 −1.00732 183 0.227055 0.460513 184 −0.06852 −0.91193 185 −0.07212 −0.84389 186 0.571736 0.309804 187 0.537941 0.265783 188 1.233532 0.810271 189 0.219658 −0.22491 190 −0.36104 0.332115 191 −0.18942 −0.1638 192 −0.59689 −0.13726 193 −0.33822 −0.20329 194 −0.2269 −0.07741 195 0.308725 −0.47266 196 0.763413 −0.09072 197 0.822728 0.866146 198 0.21017 −0.77585 199 −0.02319 0.512316 200 0.903219 −0.38413 201 −0.69516 −0.36682 202 −1.77259 −0.48219 203 −0.12357 −0.49763 204 0.268101 0.335958 205 −0.47952 −0.00869 206 −0.64648 −0.43127 207 −0.20566 0.83273 208 0.891432 0.582017 209 1.595405 0.526094 210 0.295802 0.170744 211 −0.06414 −0.06092 212 0.181292 −0.18714 213 −0.84168 −0.43137 214 0.795056 −0.82129 215 −0.17349 −0.06386 216 0.524684 −0.6431 217 0.01955 0.584466 218 0.334903 0.589175 219 0.484624 −1.27308 220 −0.2432 1.417159 221 1.328315 0.388687 222 −0.30025 −0.7474 223 −1.88373 −0.8222 224 −0.12477 −0.68928 225 0.459323 −0.1235 226 −0.024.54 0.040108 227 0.094795 −0.91173 228 0.245644 1.019559 229 0.203867 0.750493 230 0.232651 1.883079 231 0.235931 −0.1407 232 0.002532 −0.31216 233 0.793494 0.803846 234 −0.85145 −0.56047 235 0.979351 −0.42222 236 −0.06487 −0.31285 237 1.144863 −1.12495 238 −0.15415 0.123716 239 −0.26907 0.60704 240 0.417199 −0.66759 241 0.54443 0.19883 242 0.512661 0.526665 243 −0.19581 −0.69199 244 −1.83611 −0.56734 245 0.248137 −0.6183 246 0.719724 0.362173 247 −1.45562 0.896144 248 0.036063 −1.10999 249 0.276427 0.731965 250 1.563736 0.884842 251 0.355988 1.087338 252 0.17992 −0.13668 253 0.371447 −0.84377 254 0.494653 0.44325 255 −0.49123 0.280616 256 0.836888 −0.6744 257 0.306617 −0.94787 258 0.853347 −0.42568 259 0.313188 0.99838 260 −0.09518 0.606475 261 −0.24398 −0.58032 262 −0.01009 1.018463 263 0.712298 0.2833 264 0.09528 −0.97263 265 −1.83872 −0.47492 266 −0.46719 −0.38963 267 0.253523 0.75298 268 −0.99408 0.54079 269 −0.46788 −0.42138 270 0.10059 0.465181 271 1.628881 0.571075 272 0.985786 −0.09001 273 −0.17393 0.003292 274 −0.09132 −0.08775 275 0.601023 0.176045 276 −0.60317 −0.3847 277 0.59004 −0.6693 278 0.356249 −1.22756 279 1.16766 −0.20239 280 0.553931 1.286648 281 0.035759 0.291821 282 −0.43328 −0.04207 283 −0.1205 0.660251 284 0.804468 0.247399 285 0.002066 −0.56318 286 −1.33456 −0.59814 287 −0.39328 0.112915 288 −0.16621 0.528415 289 −0.78284 0.734089 290 −0.36778 −0.32289 291 −0.24177 0.30388 292 0.883634 −0.02213 293 0.526107 0.212735 294 −0.22489 −0.1385 295 0.415039 −0.90147 296 0.153491 0.352736 297 −0.11253 −0.96807 298 0.467165 −0.54412 299 −0.17126 −0.52193 300 0.788337 −0.03039 301 0.911138 1.3102 302 0.093481 −0.34812 303 −0.55441 0.029816 304 0.489211 −0.18274 305 −0.39533 0.276446 306 −0.59687 −0.2716 307 −0.99818 −0.6321 308 −0.54105 0.468147 309 0.363936 0.326605 310 −0.51659 0.208887 311 −0.94323 0.14807 312 0.044745 0.167918 313 0.677847 0.158515 314 0.659608 −0.02807 315 −0.08393 0.286155 316 0.162055 −0.23945 317 1.259513 0.195843 318 −0.05268 0.022288 319 0.545569 −0.35745 320 −0.52506 −0.16193 321 −0.35724 1.065798 322 0.149871 0.989745 323 0.155403 0.023116 324 0.180607 −0.29687 325 0.254375 −0.55448 326 −0.10757 0.616046 327 −0.21484 −0.19326 328 −1.32521 −0.04685 329 −0.52195 0.338382 330 −0.52643 1.246406 331 0.350233 −0.58487 332 −0.45791 −0.1388 333 0.242386 −0.48422 334 0.489285 −0.79099 335 0.445327 0.045959 336 0.152633 0.140344 337 −0.03022 −0.30771 338 0.632293 −0.02374 339 −0.08615 −0.03418 340 −0.44081 0.866435 341 −0.50159 −0.51748 342 0.81282 −0.01571 343 0.067787 1.553558 344 −0.47632 0.196224 345 0.387457 −0.65912 346 0.52038 −0.61349 347 −0.11048 −0.17568 348 −0.32033 −0.31679 349 −0.8788 −0.29749 350 −0.45012 0.616855 351 0.189491 −0.21047 352 −0.0252 −0.31013 353 0.09285 −0.59475 354 −0.06975 −0.37393 355 0.453887 0.055217 356 0.434582 0.847264 357 0.138895 −0.16725 358 0.460854 −0.73421 359 −0.08043 0.8153 360 −0.22652 0.363883 361 0.276865 0.1623 362 0.657328 −1.52977 363 0.277363 0.223051 364 1.130451 1.645333 365 −0.48611 0.011101 366 −0.09968 −0.25949 367 0.364756 −0.4449 368 −0.39767 0.877105 369 −0.79214 0.425876 370 −1.20164 −0.11292 371 0.281444 −0.20106 372 0.303414 0.427254 373 −0.92178 0.557361 374 0.533701 −1.18621 375 −0.15805 −0.73345 376 0.456479 0.000646 377 0.295776 0.496952 378 −0.01329 0.065039 379 −0.09384 −0.20761 380 0.274427 0.269854 381 0.188822 −0.66758 382 0.047133 −0.22507 383 −0.23114 −0.49506 384 −0.1771 0.367024 385 1.483081 1.216784 386 −0.73488 0.075664 387 −0.68143 0.103813 388 0.28584 −0.85768 389 0.930243 −0.29447 390 −0.60416 0.289829 391 −0.88622 −0.58707 392 −0.48878 0.360653 393 −0.008 0.765181 394 −0.34795 0.509356 395 0.283503 −0.64571 396 0.229828 −0.32588 397 0.897132 0.403366 398 0.805111 0.137891 399 −0.06116 −0.16817 Group 9 v(j) 0 4.981966 1 −9.82405 2 −9.23957

TABLE J Group 10 w(i, j) 1 2 0 −0.21773 0.95167 1 −0.08082 0.0675 2 0.133668 1.193804 3 0.544682 −1.04487 4 0.121715 −0.07394 5 0.326843 −0.42653 6 −0.67617 1.009579 7 0.382046 0.386103 8 1.511935 −1.72435 9 0.608665 −1.12193 10 −0.06424 0.815661 11 0.752652 −0.13895 12 −0.43834 0.581571 13 −0.86096 −0.01378 14 −0.5169 0.538929 15 −0.06988 −0.18176 16 −1.88976 0.394621 17 0.154164 0.029392 18 −0.18418 0.371262 19 0.369377 0.498222 20 0.239975 0.43862 21 0.172868 0.046495 22 −1.1767 0.339212 23 0.038298 0.411596 24 −2.11033 0.659546 25 0.298284 −0.01726 26 0.118495 −0.50437 27 0.325695 0.418034 28 0.8627 0.856154 29 0.784064 −1.05789 30 0.730496 −1.5156 31 0.343097 0.34106 32 0.395478 1.366663 33 0.199538 −0.09937 34 −1.52002 0.147602 35 −0.05017 −0.20997 36 −0.52503 0.316586 37 −0.20434 −0.97047 38 −0.11874 −0.17555 39 0.893663 −0.39776 40 −0.09813 0.417118 41 0.430623 0.189829 42 0.015809 −0.21414 43 −0.14313 0.117916 44 −0.29495 0.944132 45 −1.162 0.174987 46 0.099015 0.337924 47 −0.34787 −0.2085 48 0.515055 0.596587 49 0.340882 0.967424 50 −0.08268 0.306925 51 0.277343 −0.46136 52 −0.43352 0.970509 53 1.124498 1.18225 54 −0.14135 −0.0326 55 −1.23821 0.004672 56 0.263903 −0.90628 57 0.82547 −0.41619 58 0.02184 −0.87756 59 0.025358 −1.06669 60 0.003618 0.78061 61 0.609521 −0.26741 62 0.74983 0.028416 63 0.008452 0.234547 64 0.365827 −0.06829 65 −0.49862 0.912657 66 0.185391 −0.80148 67 0.381624 −0.30506 68 −0.7952 0.071444 69 0.924077 0.092822 70 0.367975 0.785521 71 −0.38631 0.497334 72 −0.01782 −0.77508 73 −1.16561 0.818246 74 −0.48721 1.496814 75 −0.39069 −0.2942 76 −0.60262 −1.15507 77 0.407577 0.183629 78 0.437982 −0.13769 79 −0.64203 −0.2094 80 −0.04004 −0.7484 81 0.444955 −0.02859 82 0.155416 −0.30453 83 −0.06453 0.354482 84 −0.23992 −0.1623 85 1.000023 −0.91666 86 0.323839 0.607188 87 0.398023 −0.17633 88 −0.7008 0.428521 89 −0.35049 0.471606 90 0.807497 0.234673 91 1.032899 −0.44715 92 −0.58409 0.79558 93 −0.41526 −0.77405 94 0.056802 0.402432 95 0.699936 0.246205 96 0.259323 −0.31317 97 −0.66119 −1.32467 98 0.263412 −0.57359 99 0.264639 0.284937 100 −0.50496 −0.12251 101 0.16423 −0.00587 102 −0.74334 0.738508 103 0.082901 0.745391 104 −0.4341 0.63456 105 −0.27487 −0.19392 106 −0.20281 −0.2119 107 0.401397 0.326238 108 0.238096 −0.99372 109 0.461596 −0.71014 110 −0.17323 −0.01865 111 1.113207 −0.48887 112 −0.21206 1.151766 113 −0.30801 1.118044 114 −1.27072 0.032129 115 −0.95366 0.138042 116 0.459428 0.874064 117 −0.13406 0.059186 118 −0.71757 −1.42382 119 0.05319 −0.30797 120 −0.32224 0.743598 121 −0.30567 −0.23633 122 −0.48825 −0.16081 123 0.836827 −0.52256 124 0.395397 0.466756 125 0.591145 −0.20207 126 0.263215 0.271603 127 −0.74747 0.48582 128 −0.38176 0.239157 129 0.098815 −0.6565 130 0.279631 −0.19188 131 −0.505 −0.24193 132 0.078652 0.27227 133 0.545278 1.099666 134 0.623631 0.610526 135 −0.47941 −0.73372 136 0.1908 −0.212 137 0.58491 0.802174 138 0.215447 −0.79666 139 −0.5143 −1.85654 140 0.470532 −0.92079 141 −0.12043 0.137829 142 −0.17338 −0.22141 143 −1.06062 −0.03656 144 0.671523 −0.16176 145 −0.11988 0.97522 146 0.219223 1.163602 147 −0.22213 −0.09253 148 −0.65502 0.275044 149 −0.11003 0.213207 150 −0.28553 −0.41543 151 0.019128 −0.09822 152 −0.11046 −0.0706 153 0.137203 −0.37862 154 1.491766 0.797081 155 −0.01711 1.110665 156 −0.42072 −0.45854 157 0.334536 0.052784 158 0.140428 1.078279 159 0.16883 −0.83192 160 −0.95643 −1.52285 161 −0.68153 −0.08786 162 0.624607 −0.00196 163 −0.15398 −0.59526 164 −1.39393 0.482341 165 0.473873 −0.21725 166 0.490911 −0.05932 167 0.733999 0.422976 168 −0.02329 −0.20126 169 −0.10513 −0.12856 170 0.375006 −0.36407 171 −0.33327 −0.17987 172 −0.37175 0.494296 173 0.702191 −0.7595 174 −0.16296 −0.20259 175 0.152321 0.460986 176 0.697848 0.3066 177 −0.14361 −0.67665 178 0.81453 −0.05581 179 0.687745 0.68682 180 −1.25889 0.645092 181 −0.02834 −1.93654 182 0.050488 −0.26644 183 −0.48807 0.197827 184 −0.46939 −0.29067 185 −0.33725 0.067898 186 −0.04078 0.960604 187 0.634126 −0.49156 188 −0.14168 1.674543 189 0.02444 0.098474 190 −0.14505 0.205176 191 −0.16419 0.442674 192 0.044461 −1.07263 193 −1.36962 0.37259 194 0.283042 0.017251 195 1.092625 −1.1232 196 0.247437 0.548705 197 −0.39745 1.194135 198 −0.44046 0.627115 199 0.069683 0.592096 200 0.225729 1.428233 201 −1.25359 −0.42427 202 −1.17756 −1.58033 203 0.503496 −0.76863 204 1.031094 −0.74216 205 −0.12463 −0.30107 206 0.096206 −1.13019 207 1.021226 0.31877 208 1.269505 0.67148 209 −0.46299 1.010138 210 −0.28538 −0.03308 211 −0.06883 0.204001 212 −0.01832 0.269239 213 0.297059 −1.84782 214 −0.07365 −0.21822 215 0.486585 0.0699 216 −0.83033 0.736992 217 −0.12023 1.029522 218 1.02821 0.25679 219 −0.22914 0.055263 220 1.012032 0.268538 221 −0.2231 0.942085 222 0.272282 −1.05414 223 −2.01859 −1.0958 224 −0.08049 −0.64881 225 −0.29718 0.184306 226 −0.55353 0.089595 227 −0.05476 −0.60637 228 −0.05174 1.126084 229 −0.16872 0.432311 230 0.65904 1.033112 231 −0.08572 −0.00212 232 −0.29466 −0.06132 233 0.578632 0.215785 234 −0.96778 −0.43407 235 0.002677 0.094515 236 0.193565 −0.54194 237 −0.46957 0.377909 238 1.197912 0.404643 239 −0.78557 1.067509 240 0.009357 −0.09093 241 0.488222 0.474727 242 0.52839 0.732205 243 −0.87273 −0.85902 244 −1.38837 −1.05511 245 −0.89398 0.066645 246 0.855543 −0.80416 247 0.506373 −1.26234 248 0.335109 −0.8094 249 −0.06034 0.774042 250 −0.12714 1.181986 251 0.395557 1.203972 252 0.226989 −0.16054 253 −0.58576 0.31283 254 0.182666 0.053203 255 −0.63325 −0.17037 256 0.400883 0.028283 257 0.112598 −0.59169 258 0.600046 −0.2114 259 0.50731 0.637549 260 −0.11214 0.468035 261 −0.03818 0.333437 262 0.890646 0.21398 263 1.325245 0.366913 264 −0.11456 −0.64253 265 −1.90257 −1.00335 266 −0.68849 −0.06369 267 −0.0315 0.449778 268 0.239412 −0.88748 269 0.212653 −0.81674 270 0.344784 0.58365 271 0.953292 1.068973 272 −0.71044 1.393535 273 −0.18484 −0.09612 274 0.376895 −0.20359 275 −0.64558 1.150552 276 −0.91855 −0.51135 277 1.010612 −0.55235 278 −0.52861 −0.02539 279 −0.03456 0.647398 280 0.962356 1.377247 281 −0.90009 1.121584 282 0.310246 −0.18279 283 0.03641 0.195487 284 0.119913 0.214807 285 −0.0332 −0.15499 286 −0.31766 −2.14717 287 −0.10553 −0.30634 288 0.096125 −0.07956 289 0.705596 −0.71083 290 −0.74559 −0.48972 291 −0.10237 0.925293 292 0.649804 0.455141 293 −0.47315 1.168144 294 0.119503 −0.01637 295 −0.433 0.20022 296 0.058918 0.780589 297 −0.28718 −1.12224 298 0.144755 0.160832 299 −0.40157 −0.87417 300 0.662664 0.204028 301 −0.00299 2.032077 302 0.418736 −0.58364 303 0.412196 −0.12008 304 0.169921 0.314581 305 −0.01066 −0.4368 306 −0.1617 −0.02143 307 −0.21742 −1.50086 308 −0.19351 0.038954 309 −0.34873 0.58912 310 −0.67432 0.244386 311 −0.44883 −0.0935 312 0.782133 −0.16698 313 −0.38938 0.479967 314 0.328822 0.044201 315 −0.27238 −0.18091 316 −0.06375 −0.36066 317 1.015702 1.01279 318 −1.25294 0.096562 319 −0.24241 0.341134 320 −0.20625 −0.71412 321 0.936838 −0.1063 322 0.178143 1.737094 323 −0.06339 −0.24368 324 −0.71818 0.701858 325 −0.04926 0.555514 326 0.413655 −0.31184 327 −0.07405 −0.26802 328 −1.05429 −0.66335 329 −0.67127 0.739118 330 −0.18322 −0.04423 331 0.70219 −0.67887 332 −0.21005 −0.06677 333 0.696555 −0.8612 334 −0.17799 0.40026 335 0.369617 0.059646 336 0.199605 0.276308 337 0.688028 −0.36144 338 0.366221 0.669716 339 −0.82291 −0.06005 340 −0.23427 0.030383 341 −1.87436 0.983992 342 0.037124 0.483859 343 0.931052 1.781862 344 0.55304 −0.45553 345 0.600632 −0.27261 346 0.404765 0.116244 347 −0.07397 −0.25744 348 0.647364 −1.00598 349 −0.48945 −0.85349 350 −0.08483 −0.1437 351 −0.99018 0.26505 352 −0.39191 0.282081 353 −0.26311 −0.36914 354 0.960139 −0.83258 355 −0.53822 0.811772 356 0.671682 0.385085 357 0.006271 −0.04253 358 −0.21623 0.290006 359 0.402823 0.711615 360 −0.54409 −0.14294 361 0.193133 0.309053 362 −0.97294 0.238346 363 0.399154 −0.08528 364 1.132518 2.528306 365 0.811664 −0.75203 366 0.25782 −0.12548 367 −0.10651 0.237355 368 −0.50943 0.20882 369 −0.1833 −0.8121 370 −0.59408 −1.18243 371 −0.66789 0.517471 372 0.989984 −0.7456 373 −0.12962 −0.03808 374 0.161323 −0.45044 375 −0.07859 −0.00279 376 −0.31234 0.317121 377 0.160675 0.48443 378 −0.08068 0.151237 379 0.654037 −0.45605 380 0.522271 0.924588 381 −0.68717 0.180251 382 0.783095 −0.91222 383 −0.14511 −0.14484 384 0.387458 −0.06218 385 1.21814 1.69288 386 −0.80553 0.24397 387 −0.11478 −0.50692 388 0.223987 −0.47254 389 −0.57047 0.515589 390 −0.78901 0.427246 391 −0.53284 −0.89689 392 0.139725 −0.43812 393 0.037648 0.294196 394 −0.16659 0.162129 395 −0.68619 −0.263 396 0.272476 −0.25536 397 0.015712 −0.22681 398 0.201703 0.609574 399 0.176496 −0.09298 Group 10 v(j) 0 5.761896 1 −10.274 2 −11.409 Abbreviation

-   BLAST: Basic Local Alignment Search Tool -   DSC: Determination of Secondary structure Class -   DSSP: Dictionary of Secondary Structures of Proteins -   PDB: Protein Data Bank -   PHD: Profile network from HeiDelberg -   SCOP: Structural Classification of Proteins

Embodiment 4

A non-redundant protein sequence data set whose structure is known and which has been disclosed on the Internet, nr-PDB, was prepared as a basic data set. Among data in this data set, only data including two or more domains defined in SCOP, a structural classification database, in 1 sequence was collected. The structure of the sequences were further examined, regions with a loop structure of 4 residues or more were selected, and those existing on the boundary between adjoining two domains were defined as domain linkers, while the others and not existing either of the N/C terminals were defined as non-domain linker loops, and the respective data sets were prepared.

Distribution of sequence length in the multi-domain protein data set including one or more above defined domain linkers is shown in FIG. 42. Also, the summary of the linker sequence and the non-linker loop sequence existing in the sequence data set is shown in FIG. 43.

Embodiment 5

The occurrence frequencies P_(Xaa) ^(L) and P_(Xaa) ^(N) of the amino acid X_(aa) in each data set of domain linker and non-domain linker loop are shown in FIG. 44. Using these numeral values, a probability that a linker candidate sequence can exist as a domain linker or a non-domain linker loop is calculated, respectively, and which is how much larger is indicated as a score So in the equation in FIG. 45.

Embodiment 6

As shown in FIG. 46, a pattern consisting of some types of 2 residues exists in a linker sequence. Similarly to the case for an arbitrary amino acid, this is analyzed based on the difference in occurrence frequency between the domain linker and the non-domain linker loop.

In each of the data sets for the domain linker and the non-domain linker loop prepared in Embodiment 4, occurrence probabilities P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of the amino-acid residue pair X_(aa) and Y_(aa) (the order of X_(aa) and Y_(aa) does not matter) with m pieces (m is an integer, m=0, 1, 2) of arbitrary amino-acid residues between them are shown in FIGS. 47 through 49. Using these numeral values, a probability that a linker candidate sequence can exist as a domain linker or a non-domain linker loop is calculated, respectively, and which is how much larger is indicated as a score S_(k) (k=1 through 3) in the equation in FIG. 50. The calculation of the linker degree discrimination score according to a preferred embodiment of the present application was carried out for the prepared 242 pieces of linker sequences and 3381 pieces of non-linker sequences, and the distribution of each sequence is shown in FIG. 51 with F₁s on the horizontal axis and F₁p on the vertical axis.

Embodiment 7

The results of domain linker prediction executed for the multi-domain protein data sets defined in Embodiment 4 in 6 different methods are shown in FIG. 52. The results with the best prediction efficiency were obtained when scores explained in Embodiments 5 and 6 were used in combination. The legend in the graph of FIG. 52 shows, in the order from above, the case where the threshold value is changed using the score F₁₂s, the case where the threshold value is changed using the score F₁₂ (=F₁₂s+αF₁₂p), the case where the top 1 through 10 were taken using the score F₁₂, the case where the top 1 through 10 were taken using the score F₁₂ (=F₁₂s+αF₁₂p), the case where the loop predicted by the secondary structure prediction tool DSC was predicted as a linker in the order of length, and the case where the threshold value was changed using the score F₁₁(=F₁₁s+αF₁₁p). In the graph of FIG. 52, the horizontal axis: specificity=number of linker prediction successes/prediction presented number, the vertical axis: sensitivity=number of linker prediction successes/number of existing linkers.

Embodiment 8

The Jackknife test of this predicting method was executed for the multi-domain protein data set defined in Embodiment 4. That is, the data set was divided into 5 partial sets, parameters were set using the sequence groups included in 4 of them, and domain linker prediction was made for the remaining 1 sequence group. This was repeated for the 5 partial sets. The average of correct answer rate (specificity) by this method was 35.6%.

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All the publications, patents and patent applications quoted in this specification are incorporated as they are in this specification as reference.

INDUSTRIAL APPLICABILITY

By this invention, a linker sequence of a protein can be predicted.

Also, by this invention, characteristics of a sequence of a domain linker were identified. Using these characteristics, a linker sequence can be detected in an amino-acid sequence of a protein, and as a result, a structural domain region of a protein can be predicted.

When the linker sequence can be predicted, a protein can be divided into structural domains. It is difficult to analyze the structure of a protein with large molecular weight, but if a protein can be divided into structural domains with small molecular weights, structural analysis and functional analysis per structural domain would be enabled, and functional analysis of a -protein would progress at a significant speed. 

1. A method of training a neural network to identify a linker sequence of a protein consisting of 2 or more structural domains comprising: a dividing step for dividing an amino-acid sequence of a protein consisting of 2 or more structural domains of a data set into a linker sequence and a non-linker sequence; a window setting step for taking a window of a range of 5 to 35 residues within the amino-acid sequence of the protein consisting of two or more structural domains of the data set; a sequence classifying step in which, if an amino-acid residue located at the center of the window constitutes a part of the linker sequence, a numeral value is granted to classify the amino-acid sequence in the winder as a positive sequence and if the amino-acid residue located at the center of the window constitutes a part of the non-linker sequence, a numeral value is granted to classify the amino-acid sequence in the window as a negative sequence; and a learning step for repeatedly learning to optimize a weight parameter of a hierarchical neural network by a back-propagation method, in which a value representing an amino-acid sequence in the window in numerals is input to the hierarchical neural network to acquire an output value, the error between the output value and the numeral value which classifies the amino-acid sequence in the window either as a positive sequence or as a negative sequence is calculated, and the weight parameter of the hierarchical neural network is so determined that the error becomes minimal.
 2. A method of predicting a linker sequence of a protein whose structure is unknown comprising: a window setting step for taking a window of a range of 5 to 35 residues within an amino-acid sequence of a protein whose structure is unknown; an input/output step for obtaining an output value by inputting a value of the amino-acid sequence in the window represented in numerals into a hierarchical neutral network having trained by the method of claim 1; a predicted value granting step for granting the output value to an amino-acid residue located at the center of the window as a predicted value; a step of repeating the input/output step and the predicted value granting step, with the position of the window being moved within a desired range of the amino-acid sequence of the protein whose structure is unknown; and a linker sequence predicting step for predicting as a linker sequence a region consisting of amino-acid residues with the predicted values larger than a preset threshold value.
 3. A method as set forth in claim 2 comprising, following the step of repeating the input/output step and the predicted value granting step: an average value calculating step for obtaining an average value by taking a new window of a range more than the predetermined number of residues within the amino-acid sequence of the protein whose structure is unknown and smoothing the predicted values over the amino-acid residues within this window; and a step for repeating the average value calculating step, with the position of the new window being moved within a desired range of the amino-acid sequence of the protein whose structure is unknown, and in the linker sequence predicting step, a linker sequence is predicted by the threshold with respect to the average value of the predicted values.
 4. A method as set forth in claim 3, wherein in the linker sequence predicting step, if the largest of the predicted values for the amino-acid residues in a region consisting of amino-acid residues whose average value of the predicted values, is larger than a preset threshold value is larger than a preset cut-off value, that region is predicted as a linker sequence.
 5. A system for predicting a linker sequence of a protein whose structure is unknown comprising an amino-acid sequence input means for inputting numerals that represent the amino-acid sequence of the protein whose structure is unknown, a window setting means for taking a window in the amino-acid sequence of the protein whose structure is unknown, an in-window amino-acid sequence input means by which numerals that represent the amino-acid sequence in the window are input into a hierarchical neural network trained to identify the linker sequence of a protein consisting of 2 or more structural domains, an output value calculating means for having the hierarchical neural network calculate an output value, a predicted value granting means for granting the output value to the amino-acid residue located at the center of the window as a predicted value, a window-position moving means for moving the position of the window within a desired range of the amino-acid sequence of the protein whose structure is unknown, a smoothing window setting means for taking a new window of a range more than the predetermined number of residues in the amino-acid sequence of the protein whose structure is unknown, an average value calculating means for obtaining an average value by smoothing predicted values over the amino-acid residues in the new window, a smoothing window moving means for moving the position of the new window within a desired range of the amino-acid sequence of the protein whose structure is unknown, and a linker sequence predicting means for predicting as a linker sequence a region consisting of the amino-acid residues whose average value of the predicted values is larger than a preset threshold value.
 6. A program for having a computer function as a system for predicting a linker sequence of a protein whose structure is unknown characterized in that the system comprises an amino-acid sequence input means for inputting numerals that represent the amino-acid sequence of the protein whose structure is unknown, a window setting means for taking a window in the amino-acid sequence of the protein whose structure is unknown, an in-window amino-acid sequence input means by which numerals that represent the amino-acid sequence in the window are input into a hierarchical neural network trained to identify the linker sequence of a protein consisting of 2 or more structural domains, an output value calculating means for having the hierarchical neural network calculate an output value, a predicted value granting means for granting the output value to the amino-acid residue located at the center of the window as a predicted value, a window-position moving means for moving the position of the window within a desired range of the amino-acid sequence of the protein whose structure is unknown, a smoothing window setting means for taking a new window of a range more than the predetermined number of residues in the amino-acid sequence of the protein whose structure is unknown, an average value calculating means for obtaining an average value by smoothing predicted values over the amino-acid residues in the new window, a smoothing window moving means for moving the position of the new window within a desired range of the amino-acid sequence of the protein whose structure is unknown, and a linker sequence predicting means for predicting as a linker sequence a region consisting of the amino-acid residues whose average value of the predicted values is larger than a preset threshold value.
 7. A computer readable recording medium having recorded thereon a program for having a computer function as a system for predicting a linker sequence of a protein whose structure is unknown characterized in that the system comprises an amino-acid sequence input means for inputting numerals that represent the amino-acid sequence of the protein whose structure is unknown, a window setting means for taking a window in the amino-acid sequence of the protein whose structure is unknown, an in-window amino-acid sequence input means by which numerals that represent the amino-acid sequence in the window are input into a hierarchical neural network trained to identify the linker sequence of a protein consisting of 2 or more structural domains, an output value calculating means for having the hierarchical neural network calculate an output value, a predicted value granting means for granting the output value to the amino-acid residue located at the center of the window as a predicted value, a window-position moving means for moving the position of the window within a desired range of the amino-acid sequence of the protein whose structure is unknown, a smoothing window setting means for taking a new window of a range more than the predetermined number of residues in the amino-acid sequence of the protein whose structure is unknown, an average value calculating means for obtaining an average value by smoothing predicted values over the amino-acid residues in the new window, a smoothing window moving means for moving the position of the new window within a desired range of the amino-acid sequence of the protein whose structure is unknown, and a linker sequence predicting means for predicting as a linker sequence a region consisting of the amino-acid residues whose average value of the predicted values is larger than a preset threshold value.
 8. A method of producing a protein fragment corresponding to one or more structural domains located closer to the N-terminal side than a predicted linker sequence comprising a step for producing at least one of the protein fragments obtained by cutting off a protein at any of the following portions (i), (ii) or (iii): (i) an arbitrary portion of at least one linker sequence predicted by the method as set forth in claim 2; (ii) any of portions located between the C-terminal of at least one linker sequence predicted by the method as set forth in claim 2 and the 50^(th) amino-acid residue as counted therefrom to the C-terminal side of the protein; or (iii) any of portions located between the N-terminal of at least one linker sequence predicted by the method as set forth in claim 2 and the 15^(th) amino-acid residue as counted therefrom to the N-terminal side of the protein.
 9. A method of producing a protein fragment corresponding to one or more structural domains located closer to the C-terminal side than a predicted linker sequence comprising a step for producing at least one of the protein fragments obtained by cutting off a protein at any of the following portions (i), (iv) or (v): (i) an arbitrary portion of at least one linker sequence predicted by the method as set forth in claim 2; (iv) any of portions located between the N-terminal of at least one linker sequence predicted by the method as set forth in claim 2 and the 50^(th) amino-acid residue as counted therefrom to the N-terminal side of the protein; or (v) any of portions located between the C-terminal of at least one linker sequence predicted by the method as set forth in claim 2 and the 15^(th) amino-acid residue as counted therefrom to the C-terminal side of the protein.
 10. A method of analyzing a protein fragment corresponding to one or more structural domains located closer to the N-terminal side than a predicted linker sequence comprising a step for analyzing at least one of the protein fragments obtained by cutting off a protein at any of the following portions (i), (ii) or (iii): (i) an arbitrary portion of at least one linker sequence predicted by the method as set forth in claim 2; (ii) any of portions located between the C-terminal of at least one linker sequence predicted by the method as set forth in claim 2 and the 50^(th) amino-acid residue as counted therefrom to the C-terminal side of the protein; or (iii) any of portions located between the N-terminal of at least one linker sequence predicted by the method as set forth in claim 2 and the 15^(th) amino-acid residue as counted therefrom to the N-terminal side of the protein.
 11. A method of analyzing a protein fragment corresponding to one or more structural domains located closer to the C-terminal side than a predicted linker sequence comprising a step for analyzing at least one of the protein fragments obtained by cutting off a protein at any of the following portions (i), (iv) or (v): (i) an arbitrary portion of at least one linker sequence predicted by the method as set forth in claim 2; (iv) any of portions located between the N-terminal of at least one linker sequence predicted by the method as set forth in claim 2 and the 50^(th) amino-acid residue counted therefrom to the N-terminal side of the protein; or (v) any of portions located between the C-terminal of at least one linker sequence predicted by the method as set forth in claim 2 and the 15^(th) amino-acid residue as counted therefrom to the C-terminal side of the protein.
 12. A method of constructing a linker sequence database comprising a step for recording in a recording medium the amino-acid sequence data for the linker sequence predicted by the method as set forth in claim
 2. 13. A method of constructing a structural domain database comprising a step for recording in a recording medium the amino-acid sequence data for the structural domain obtained by cutting off a protein at an arbitrary portion of at least one linker sequence predicted by the method as set forth in claim
 2. 14. A peptide which has a sequence pattern satisfying the conditions of (i) and (ii) below and can function as a domain linker of a multi-domain protein: (i) when a sequence fragment consisting of 19 residues in succession is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε 0,1} (i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit (=19×21) binary sequence obtained as a result of arrangement in series of 21-bit binary sequences associated with amino acid types according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine (G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” in that order and for the 21-bit binary sequence, only those matching the amino acid types of the represented residues are 1, while the others are 0), the value of the following g(x) should be in a range of 0.5 to 1.0: g(x) = τ  (v₀ + v₁f₁(x) + v₂f₂(x)) ${f_{j}(x)} = {\tau\quad\left( {w_{0\quad j} + {\sum\limits_{i = 1}^{399}\quad{w_{ij}x_{i}}}} \right)\quad\left( {{j = 1},2} \right)}$ τ  (u) = 1/(1 + 𝕖^(−u)) (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and v_(j)(j=0, 1, 2) is selected from the group consisting of the combinations of Group 1 in Table A, the combinations of Group 2 in Table B, the combinations of Group 3 in Table C, the combinations of Group 4 in Table D, the combinations of Group 5 in Table E, the combinations of Group 6 in Table F, the combinations of Group 7 in Table G, the combinations of Group 8 in Table H, the combinations of group 9 in Table I, and the combinations of Group 10 in Table J); (ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 should be included, with an amino acid within 9 residues before and after the central residue being optionally further included.
 15. A method of predicting a region having a sequence pattern satisfying the conditions of (i) and (ii) below as a linker sequence of protein: (i) when a sequence fragment consisting of 19 residues in succession is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε 0,1} (i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit (=19×21) binary sequence obtained as a result of arrangement in series of 21-bit binary sequences associated with amino acid types according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine (G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” in that order and for the 21-bit binary sequence, only those matching the amino acid types of the represented residues are 1, while the others are 0), the value of the following g(x) should be in a range of 0.5 to 1.0: g(x) = τ  (v₀ + v₁f₁(x) + v₂f₂(x)) ${f_{j}(x)} = {\tau\quad\left( {w_{0\quad j} + {\sum\limits_{i = 1}^{399}\quad{w_{ij}x_{i}}}} \right)\quad\left( {{j = 1},2} \right)}$ τ  (u) = 1/(1 + 𝕖^(−u)) (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and v_(j)(j=0, 1, 2) is selected from the group consisting of the combinations of Group 1 in Table A, the combinations of Group 2 in Table B, the combinations of Group 3 in Table C, the combinations of Group 4 in Table D, the combinations of Group 5 in Table E, the combinations of Group 6 in Table F, the combinations of Group 7 in Table G, the combinations of Group 8 in Table H, the combinations of group 9 in Table I, and the combinations of Group 10 in Table J); (ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 should be included, with an amino acid within 9 residues before and after the central residue being optionally further included.
 16. A method of dividing a protein into structural domains characterized in that the protein is cut off at an arbitrary portion of a region having a sequence pattern satisfying the conditions of (i) and (ii) below: (i) when a sequence fragment consisting of 19 residues in succession is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε 0,1} (i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit (=19×21) binary sequence obtained as a result of arrangement in series of 21-bit binary sequences associated with amino acid types according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine (G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” in that order and for the 21-bit binary sequence, only those matching the amino acid types of the represented residues are 1, while the others are 0), the value of the following g(x) sould be in a range of 0.5 to 1.0: g(x) = τ  (v₀ + v₁f₁(x) + v₂f₂(x)) ${f_{j}(x)} = {\tau\quad\left( {w_{0\quad j} + {\sum\limits_{i = 1}^{399}\quad{w_{ij}x_{i}}}} \right)\quad\left( {{j = 1},2} \right)}$ τ  (u) = 1/(1 + 𝕖^(−u)) (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and v_(j)(j=0, 1, 2) is selected from the group consisting of the combinations of Group 1 in Table A, the combinations of Group 2 in Table B, the combinations of Group 3 in Table C, the combinations of Group 4 in Table D, the combinations of Group 5 in Table E, the combinations of Group 6 in Table F, the combinations of Group 7 in Table G, the combinations of Group 8 in Table H, the combinations of group 9 in Table I, and the combinations of Group 10 in Table J); (ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 should be included, with an amino acid within 9 residues before and after the central residue being optionally further included.
 17. A method of producing a protein fragment comprising a step for producing at least one of the protein fragments obtained by cutting off a protein at an arbitrary portion of a region having a sequence pattern satisfying the conditions of (i) and (ii) below: (i) when a sequence fragment consisting of 19 residues in succession is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε 0,1} (i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit (=19×21) binary sequence obtained as a result of arrangement in series of 21-bit binary sequences associated with amino acid types according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine (G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” in that order and for the 21-bit binary sequence, only those matching the amino acid types of the represented residues are 1, while the others are 0), the value of the following g(x) should be in a range of 0.5 to 1.0: g(x) = τ(v₀ + v₁f₁(x) + v₂f₂(x)) ${f_{j}(x)} = {{\tau\left( {w_{0j} + {\sum\limits_{i = 1}^{399}\quad{w_{ij}x_{i}}}} \right)}\left( {{j = 1},2} \right)}$ τ(u) = 1/(1 + 𝕖^(−u)) (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and v_(j)(j=0, 1, 2) is selected from the group consisting of the combinations of Group 1 in Table A, the combinations of Group 2 in Table B, the combinations of Group 3 in Table C, the combinations of Group 4 in Table D, the combinations of Group 5 in Table E, the combinations of Group 6 in Table F, the combinations of Group 7 in Table G, the combinations of Group 8 in Table H, the combinations of group 9 in Table I, and the combinations of Group 10 in Table J); (ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 should be included, with an amino acid within 9 residues before and after the central residue being optionally further included.
 18. A method of analyzing a protein fragment comprising a step for analyzing at least one of the protein fragments obtained by cutting off protein at an arbitrary portion of a region having a sequence pattern satisfying the conditions of (i) and (ii) below: (i) when a sequence fragment consisting of 19 residues in succession is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε 0,1} (i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit (=19×21) binary sequence obtained as a result of arrangement in series of 21-bit binary sequences associated with amino acid types according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine (G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” in that order and for the 21-bit binary sequence, only those matching the amino acid types of the represented residues are 1, while the others are 0), the value of the following g(x) should be in a range of 0.5 to 1.0: g(x) = τ(v₀ + v₁f₁(x) + v₂f₂(x)) ${f_{j}(x)} = {{\tau\left( {w_{0j} + {\sum\limits_{i = 1}^{399}\quad{w_{ij}x_{i}}}} \right)}\left( {{j = 1},2} \right)}$ τ(u) = 1/(1 + 𝕖^(−u)) (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and v_(j)(j=0, 1, 2) is selected from the group consisting of the combinations of Group 1 in Table A, the combinations of Group 2 in Table B, the combinations of Group 3 in Table C, the combinations of Group 4 in Table D, the combinations of Group 5 in Table E, the combinations of Group 6 in Table F, the combinations of Group 7 in Table G, the combinations of Group 8 in Table H, the combinations of group 9 in Table I, and the combinations of Group 10 in Table J); (ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 should be included, with an amino acid within 9 residues before and after the central residue being optionally further included.
 19. A method of producing a new multi-domain protein by designing a new linker sequence with a peptide having a sequence pattern satisfying the conditions of (i) and (ii) below and by connecting at least two protein fragments: (i) when a sequence fragment consisting of 19 in succession is represented numerically by an equation x: x=(x ₁ , x ₂ , . . . , x ₃₉₉)(x _(i) ε 0,1} (i=1, . . . , 399)) (where, x=(x₁, x₂, . . . , x₃₉₉) is a 399-bit (=19×21) binary sequence obtained as a result of arrangement in series of 21-bit binary sequences associated with amino acid types according to the sequence of the 19 residues of the sequence fragment, and the bit sequence corresponds to “alanine (A), cysteine (C), aspartic acid (D), glutamic acid (E), phenylalanine (F), glycine (G), histidine (H), isoleucine (I), lysine (K), leucine (L), methionine (M), asparagines (N), proline (P), glutamine (Q), arginine (R), serine (S), threonine (T), valine (V), tryptophan (W), tyrosine (Y), others (X)” in that order and for the 21-bit binary sequence, only those matching the amino acid types of the represented residues are 1, while the others are 0), the value of the following g(x) should be in a range of 0.5 to 1.0: g(x) = τ(v₀ + v₁f₁(x) + v₂f₂(x)) ${f_{j}(x)} = {{\tau\left( {w_{0j} + {\sum\limits_{i = 1}^{399}\quad{w_{ij}x_{i}}}} \right)}\left( {{j = 1},2} \right)}$ τ(u) = 1/(1 + 𝕖^(−u)) (where a combination of w_(ij)(i=0, . . . , 399; j=1,2) and v_(j)(j=0, 1, 2) is selected from the group consisting of the combinations of Group 1 in Table A, the combinations of Group 2 in Table B, the combinations of Group 3 in Table C, the combinations of Group 4 in Table D, the combinations of Group 5 in Table E, the combinations of Group 6 in Table F, the combinations of Group 7 in Table G, the combinations of Group 8 in Table H, the combinations of group 9 in Table I, and the combinations of Group 10 in Table J); (ii) a central residue of the sequence fragment x=(x₁, x₂, . . . , x₃₉₉) with the value of g(x) in the range of 0.5 to 1.0 should be included, with an amino acid within 9 residues before and after the central residue being optionally further included.
 20. A method comprising: i) a step for extracting a linker sequence and a non-linker loop sequence from a database of multi-domain proteins of known structures; and ii) a step for obtaining, based on statistical processing of amino-acid sequence of each domain, the probabilities P_(Xaa) ^(L) and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa) (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are the probabilities of the amino-acid residue X_(aa) occurring in a linker sequence and a non-linker loop sequence, respectively) and the probabilities P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of the amino-acid residues X_(aa) and Y_(aa) as interrupted by m (m is an integer, m=0, 1, 2) arbitrary amino-acid residues (where P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are the probabilities of the amino-acid residues X_(aa) and Y_(aa) occurring in the linker sequence and the non-linker loop sequence, respectively, as interrupted by m amino acid residues (the order of X_(aa) and Y_(aa) does not matter)), said method predicting and/or detecting a linker sequence in a multi-domain protein of unknown structure from the characteristics in terms of the amino-acid sequence of the linker sequence extracted in step i).
 21. A system comprising: i) a means for extracting a linker sequence and a non-linker loop sequence from a database of multi-domain proteins of known structures i; and ii) a means for obtaining, based on statistical processing of amino-acid sequence of each domain, the probabilities P_(Xaa) ^(L) and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa) (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are the probabilities of the amino-acid residue X_(aa) occurring in a linker sequence and a non-linker loop sequence, respectively) and the probabilities P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of the amino-acid residues X_(aa) and Y_(aa) as interrupted by m (m is an integer, m=0, 1, 2) arbitrary amino-acid residues (where P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are the probabilities of the amino-acid residues X_(aa) and Y_(aa) occurring in the linker sequence and then-linker loop sequence, respectively, as interrupted by m amino acid residues (the order of X_(aa) and Y_(aa) does not matter)), said system predicting and/or detecting a linker sequence in a multi-domain protein of unknown structure from the characteristics in terms of the amino-acid sequence of the linker sequence extracted by the means of i).
 22. A program for having a computer function as a system for predicting and/or detecting a linker sequence in a multi-domain protein of unknown structure from the characteristics in terms of its amino acid sequence, the system comprising: i) a means for extracting a linker sequence and a non-linker loop sequence from a database of multi-domain proteins of known structures; and ii) a means for obtaining, based on statistical processing of amino-acid sequence of each domain, the probabilities P_(Xaa) ^(L) and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa) (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are the probabilities of the amino-acid residue X_(aa) occurring in a linker sequence and a non-linker loop sequence, respectively) and the probabilities P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of the amino-acid residues X_(aa) and Y_(aa) as interrupted by m (m is an integer, m=0, 1, 2) arbitrary amino-acid residues (where P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are the probabilities of the amino-acid residues X_(aa) and Y_(aa) occurring in the linker sequence and the non-linker loop sequence, respectively, as interrupted by m amino acid residues (the order of X_(aa) and Y_(aa) does not matter)).
 23. A structural domain predicting method comprising a step in which a protein fragment generated by cutting off a multi-domain protein of unknown structure at any of the portions of a linker sequence in the multi-domain protein after it was predicted by the method as set forth in claim 20 is predicted as a structural domain.
 24. A protein producing method comprising a step for producing a protein having the same amino-acid sequence as the structural domain predicted by the method as set forth in claim
 23. 25. A protein analyzing method comprising a step for analyzing a protein having the same amino-acid sequence as the structural domain predicted by the method as set forth in claim
 23. 26. A system for calculating a parameter of an occurrence trend of an amino-acid residue comprising: i) a means for extracting a linker sequence and a non-linker loop sequence from a database of multi-domain proteins of known structures; ii) a means for obtaining, based on statistical processing of amino-acid sequence of each domain, the probabilities P_(Xaa) ^(L) and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa) (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are the probabilities of the amino acid residue X_(aa) occurring in a linker sequence and a non-linker loop sequence, respectively) iii) a means for obtaining an occurrence trend parameter S_(Xaa) of the amino-acid residue X_(aa) by the following equation: S _(Xaa)=log(P _(Xaa) ^(L) /P _(Xaa) ^(N)) (where S_(Xaa)=0 if there is no statistically significant difference between P_(Xaa) ^(L) and P_(Xaa) ^(N)).
 27. A program for having a computer function as a system for calculating a parameter representing an occurrence trend of an arbitrary amino-acid residue, the system comprising: i) a means for extracting a linker sequence and a non-linker loop sequence from a database of multi-domain proteins of known structures; ii) a means for obtaining, based on statistical processing of amino-acid sequence of each domain, the probabilities P_(Xaa) ^(L) and P_(Xaa) ^(N) of occurrence of an amino-acid residue X_(aa) (where P_(Xaa) ^(L) and P_(Xaa) ^(N) are the probabilities of the amino acid residue X_(aa) occurring in a linker sequence and a non-linker loop sequence, respectively); and iii) a means for obtaining an occurrence trend parameter S_(Xaa) of the amino acid residue X_(aa) by the following equation: S _(Xaa)=log(P _(Xaa) ^(L) /P _(Xaa) ^(N)) (where S_(Xaa)=0 if there is no statistically significant difference between P_(Xaa) ^(L) and P_(Xaa) ^(N)).
 28. A system for calculating a parameter of an appearance trend of an amino-acid residue pair comprising: i) a means for extracting a linker sequence and a non-linker loop sequence from a database of multi-domain proteins of known structures; ii) a means for obtaining, based on statistical processing of amino acid sequence of each domain, the probabilities P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of amino-acid residues X_(aa) and Y_(aa) (the order of X_(aa) and Y_(aa) does not matter) as interrupted by m (m is an integer, m=0, 1, 2) arbitrary amino-acid residues (where P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are the probabilities of the amino-acid residues X_(aa) and Y_(aa) occurring (the order of X_(aa) and Y_(aa) does not matter) in a linker sequence and a non-linker loop sequence, respectively, as interrupted by m amino-acid residues (m is an integer, m=0, 1, 2)) for the cases where m is 0, 1 and 2, respectively; and iii) a means for obtaining an occurrence trend parameter S_(XaaYaa(m)) of the pair of amino acid residues X_(aa) and Y_(aa) by the following equation: S _(XaaYaa(m))=log(P _(XaaYaa(m)) ^(L) /P _(XaaYaa(m)) ^(N)) (where S_(Xaa)=0 if there is no statistically significant difference between P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N)).
 29. A program for having a computer function as a system for calculating a parameter representing an occurrence trend of an arbitrary amino-acid residue pair, the system comprising: i) a means for extracting a linker sequence and a non-linker loop sequence from a database of multi-domain proteins of known structures; ii) a means for obtaining, based on statistical processing of amino acid sequence of each domain, the probabilities P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) of occurrence of amino-acid residues X_(aa) and Y_(aa) (the order of X_(aa) and Y_(aa) does not matter) as interrupted by m (m is an integer, m=0, 1, 2) arbitrary amino-acid residues (where P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N) are the probabilities of the amino-acid residues X_(aa) and Y_(aa) occurring (the order of X_(aa) and Y_(aa) does not matter) in a linker sequence and a non-linker loop sequence, respectively, as interrupted by m amino-acid residues (m is an integer, m=0, 1, 2)) for the cases where m is 0, 1 and 2, respectively; and iii) a means for obtaining an occurrence trend parameter S_(XaaYaa(m)) of the pair of amino-acid residues X_(aa) and Y_(aa) by the following equation: S _(XaaYaa(m))=log(P _(XaaYaa(m)) ^(L) /P _(XaaYaa(m)) ^(N)) (where S_(Xaa)=0 if there is no statistically significant difference between P_(XaaYaa(m)) ^(L) and P_(XaaYaa(m)) ^(N)).
 30. A system for obtaining a linker degree determination score F₁ for an amino-acid sequence with L₁ amino-acid residues (L₁ is an integer of 1 or more but not more than 21), the system comprising: i) a means for obtaining a linker trend score F₁s of an amino-acid residue A_(k) by the following equation: ${F_{1}s} = {\left( {\sum\limits_{k = 1}^{L_{1}}\quad S_{Ak}} \right)/L_{1}}$ (where S_(Ak)=log(P_(Ak) ^(L)/P_(Ak) ^(N)) where S_(Ak)=0 if there is no statistically significant difference between P_(Ak) ^(L) and P_(Ak) ^(N); P_(Ak) ^(L) and P_(Ak) ^(N) are the probabilities of the amino-acid residue A_(k) occurring in a linker sequence and a non-linker loop sequence, respectively); ii) a means for obtaining a linker trend score F₁p of the pair of amino-acid residues A_(k) and A_(k+(m+1)), as interrupted by m arbitrary amino-acid residues (m is an integer, m=0, 1, 2), by the following equation: ${F_{1}p} = {\sum\limits_{k = 1}^{L_{1}}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{{AkAk} + {({m + 1})}}(m)} + {S_{{AkAk} \cdot {({m + 1})}}(m)}} \right)/2}} \right)/L_{1}}}$ (where S_(AkAk+(m+1)(m))=log(P_(AkAk+(m+1)(m)) ^(L)/P_(AkAk+(m+1)(m)) ^(N)) and S_(AkAk−(m+1)(m))=log(P_(AkAk−(m+1)(m)) ^(L)/P_(AkAk−(m+1)(m)) ^(N)) where S_(AkAk+(m+1)(m))=0 or S_(AkAk−(m+1)(m))=0 if there is no statistically significant difference between P_(AkAk+(m+1)(m)) ^(L) and P_(AkAk+(m+1)(m)) ^(N) or between P_(AkAk−(m+1)(m)) ^(L) and P_(AkAk−(m+1)(m)) ^(N); P_(AkAk+(m+1)(m)) ^(L) and P_(AkAk+(m+1)(m)) ^(N) are the probabilities of the arbitrary amino-acid residues A_(k) and A_(k+(m+1)) occurring in a linker sequence and a non-linker loop sequence, respectively (the order of A_(k) and A_(k+(m+1)) does not matter), and P_(AkAk−m+1)(m)) ^(L) and P_(AkAk−(m+1)(m)) ^(N) are the probabilities of the arbitrary amino-acid residues A_(k) and A_(k−(m+1)) occurring in the linker sequence and the non-linker loop sequence, respectively (the order of A_(k) and A_(k−(m+1)) occurring does not matter)); and iii) a means for obtaining a linker degree determination score F₁ by the following equation below: F ₁ =F ₁ s+α ₁ F ₁ p (where 0≦α₁≦1).
 31. A program for having a computer function as a system for obtaining a linker degree determination score F₁ for an amino-acid sequence with L₁ amino-acid residues (L₁ is an integer of 1 or more but not more than 21), the system comprising: i) a means for obtaining a linker trend score F₁s of an amino-acid residue A_(k) by the following equation: ${F_{1}s} = {\left( {\sum\limits_{k = 1}^{L_{1}}\quad S_{Ak}} \right)/L_{1}}$ (where S_(Ak)=log(P_(Ak) ^(L)/P_(Ak) ^(N)) where S_(Ak)=0 if there is no statistically significant difference between P_(Ak) ^(L) and P_(Ak) ^(N); P_(Ak) ^(L) and P_(Ak) ^(N) are the probabilities of the amino-acid residue A_(k) occurring in a linker sequence and a non-linker loop sequence, respectively); ii) a means for obtaining a linker trend score F₁p of the pair of amino-acid residues A_(k) and A_(k+(m+1)), as interrupted by m arbitrary amino-acid residues (m is an integer, m=0, 1, 2), by the following equation: ${F_{1}p} = {\sum\limits_{k = 1}^{L_{1}}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{{AkAk} + {({m + 1})}}(m)} + {S_{{AkAk} - {({m + 1})}}(m)}} \right)/2}} \right)L_{1}}}$ (where S_(AkAk+(m+1)(m))=log(P_(AkAk+(m+1)(m)) ^(L)/P_(AkAk+(m+1)(m)) ^(N)) and S_(AkAk−(m+1)(m))=log(P_(AkAk−(m+1)(m)) ^(L)/P_(AkAk−(m+1)(m)) ^(N)) where S_(AkAk+(m+1)(m))=0 or S_(AkAk−(m+1)(m))=0 if there is no statistically significant difference between P_(AkAk+(m+1)(m)) ^(L) and P_(AkAk+(m+1)(m)) ^(N) or between P_(AkAk−(m+1)(m)) ^(L) and P_(AkAk−(m+1)(m)) ^(N); P_(AkAk+(m+1)(m)) ^(L) and P_(Ak+(m+1)(m)) ^(N) are the probabilities of the arbitrary amino-acid residues A_(k) and A_(k+(m+1)) occurring in a linker sequence and a non-linker loop sequence, respectively (the order of A_(k) and A_(k+(m+1)) does not matter), and P_(AkAk−(m+1)(m)) ^(L) and P_(AkAk−(m+1)(m)) ^(N) are the probabilities of the arbitrary amino-acid residues A_(k) and A_(k(m+1)) occurring in the linker sequence and the non-linker loop sequence, respectively (the order of A_(k) and A_(k(m+1)) does not matter)); and iii) a means for obtaining a linker degree determination score F₁ by the following equation: F ₁ =F ₁ s+α ₁ F ₁ p (where 0≦α₁≦1).
 32. A method of obtaining a linker degree determination score F₁₁(i) for an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) by taking a window of w amino-acid residues before and after the amino-acid residue at the position i (i is an integer of 1 or more but not more than L₂) comprising: i) a step for obtaining a linker trend determination score F₁₁s(i) of an amino-acid residue A_(k) by the following equation: ${F_{11}{s(i)}} = {\left( {\sum\limits_{k = {i \cdot w}}^{i + w}\quad S_{Ak}} \right)/W}$ (where W is the window width, and W=2w+1, S_(Ak)=log(P_(Ak) ^(L)/P_(Ak) ^(N)) where S_(Ak)=0 if there is no statistically significant difference between P_(Ak) ^(L) and P_(Ak) ^(N); P_(Ak) ^(L) and P_(Ak) ^(N) are the probabilities of the amino-acid residue A_(k) occurring in a linker sequence and a non-linker loop sequence, respectively); ii) a step for obtaining the linker trend score F₁₁p(i) of the pair of amino-acid residues A_(i) and A_(i+(m+1)), as interrupted by m arbitrary amino-acid residues (m is an integer, m=0, 1, 2), by the following equation: ${F_{11}{p(i)}} = {\sum\limits_{k = {i \cdot w}}^{i + w}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{{AiAi} + {({m + 1})}}(m)} + {S_{{AiAi} - {({m + 1})}}(m)}} \right)/2}} \right)/W}}$ (where S_(AiAi+(m+1)(m))=log(P_(AiAi+(m+1)(m)) ^(L)/P_(AiAi+(m+1)(m)) ^(N)) and S_(AiAi−(m+1)(m))=log(P_(AiAi−(m+1)(m)) ^(L)/P_(AiAi−(m+1)(m)) ^(N)) where S_(AiAi+(m+1)(m))=0 or S_(AiAi−(m+1)(m))=0 if there is no statistically significant difference between P_(AiAi+(m+1)(m)) and P_(AiAi+(m+1)(m)) ^(N) or between P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N); P_(AiAi+(m+1)(m)) ^(L) and P_(AiAi+(m+1)(m)) ^(N) are the probabilities of the pair of the arbitrary amino-acid residues A_(i) and A_(i+(m+1)) occurring in a linker sequence and a non-linker loop sequence, respectively (the order of A_(i) and A_(i+(m+1)) does not matter), and P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N) are the probabilities of the pair of the arbitrary amino-acid residues A_(i) and A_(i−(m+1)) occurring in the linker sequence and the non-linker loop sequence, respectively (the order of A_(i) and A_(i−(m+1)) does not matter)); and iii) a step for obtaining the linker degree determination score F₁₁(i) of the amino-acid residue Ai at the position i by the following equation: F ₁₁(i)=F ₁₁ s(i)+α₁₁ F ₁₁ p(i) (where 0≦α₁₁≦1).
 33. A system for obtaining a linker degree determination score F₁₁(i) for an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) by taking a window of w amino-acid residues before and after the amino-acid residue at the position i (i is an integer of 1 or more but not more than L₂) comprising: i) a step for obtaining a linker trend determination score F₁₁s(i) of an amino-acid residue A_(k) by following equation: ${F_{11}{s(i)}} = {\left( {\sum\limits_{k = {i \cdot w}}^{i + w}\quad S_{Ak}} \right)/W}$ (where W is the window width, and W=2w+1□ S_(Ak)=log(P_(Ak) ^(L)/P_(Ak) ^(N)) where S_(Ak)=0 if there is no statistically significant difference between P_(Ak) ^(L) and P_(Ak) ^(N); P_(Ak) ^(L) and P_(Ak) ^(N) are the probabilities of the amino-acid residue A_(k) occurring in a linker sequence and a non-linker loop sequence, respectively); ii) a step for obtaining the linker trend score F₁₁p(i) of the pair of amino-acid residues A_(i) and A_(i+(m+1)), as interrupted by m arbitrary amino-acid residues (m is an integer, m=0, 1, 2), by the following equation: ${F_{11}{p(i)}} = {\sum\limits_{k = {i - w}}^{i + w}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{{AiAi} + {({m + 1})}}(m)} + {S_{{AiAi} - {({m + 1})}}(m)}} \right)/2}} \right)/W}}$ (where S_(AiAi+(m+1)(m))=log(P_(AiAi+(m+1)(m)) ^(L)/P_(AiAi+(m+1)(m)) ^(N)) and S_(AiAi−(m+1)(m))=log(P_(AiAi−(m+1)(m)) ^(L)/P_(AiAi(m+1)(m)) ^(N)) where S_(AiAi+(m+1)(m))=0 or S_(AiAi−(m+1)(m))=0 if there is no statistically significant difference between P_(AiAi+(m+1)(m)) ^(L) and P_(AiAi+(m+)(m)) ^(N) or between P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N); P_(AiAi+(m+1)(m)) ^(L) and P_(AiAi+(m+)(m)) ^(N) are the probabilities of the pair of the arbitrary amino-acid residues A_(i) and A_(i+(m+1)) occurring in a linker sequence and a non-linker loop sequence, respectively (the order of A_(i) and A_(i+(m+1)) does not matter), and P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N) are the probabilities of the pair of the arbitrary amino-acid residues A_(i) and A_(i−(m+1)) occurring in the linker sequence and the non-linker loop sequence, respectively (the order of A_(i) and A_(i−(m+1)) does not matter)); and iii) a step for obtaining the linker degree determination score F₁₁(i) of the amino-acid residue Ai at the position i by the following equation: F ₁₁(i)=F ₁₁ s(i)+α₁₁ F ₁₁ p(i) (where 0≦α₁₁≦1).
 34. A program for having a computer function as a system for obtaining a linker degree determination score F₁₁(i) for an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) by taking a window of w amino-acid residues before and after the amino-acid residue at the position i (i is an integer of 1 or more but not more than L₂), the system comprising: i) a step for obtaining a linker trend score F₁₁s(i) of an amino-acid residue A_(k) by the following equation: ${F_{11}{s(i)}} = {\left( {\sum\limits_{k = {i - w}}^{\quad{i + w}}\quad S_{Ak}} \right)/W}$ (where W is the window width, and W=2w+1, S_(Ak)=log(P_(Ak) ^(L)/P_(Ak) ^(N)) where S_(Ak)=0 if there is no statistically significant difference between P_(Ak) ^(L) and P_(Ak) ^(N); P_(Ak) ^(L) and P_(Ak) ^(N) are the probabilities of the amino-acid residue A_(k) occurring in a linker sequence and a non-linker loop sequence, respectively); ii) a step for obtaining the linker trend score F₁₁p(i) of the pair of amino-acid residues A_(i) and A_(i+(m+1)), as interrupted by m arbitrary amino-acid residues (m is an integer, m=0, 1, 2), by the following equation: ${F_{11}{p(i)}} = {\sum\limits_{k = {i - w}}^{i + w}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{{AiAi} + {({m + 1})}}(m)} + {S_{{AiAi} - {({m + 1})}}(m)}} \right)/2}} \right)/W}}$ (where S_(AiAi+(m+1)(m))=log(P_(AiAi+(m+1)(m)) ^(L)/P_(AiAi+(m+1)(m)) ^(N)) and S_(AiAi−(m+1)(m))=log(P_(AiAi−(m+1)(m)) ^(L)/P_(AiAi(m+1)(m)) ^(N)) where S_(AiAi+(m+1)(m))=0 or S_(AiAi−(m+1)(m))=0 if there is no statistically significant difference between P_(AiAi+(m+1)(m)) ^(L) and P_(AiAi+(m+1)(m)) ^(N) or between P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N); P_(AiAi+(m+1)(m)) ^(L) and P_(AiAi+(m+1)(m)) ^(N) are the probabilities of the pair of the arbitrary amino-acid residues A_(i) and A_(i+(m+1)) occurring in a linker sequence and a non-linker loop sequence, respectively (the order of A_(i) and A_(i+(m+1)) does not matter), and P_(AiAi−(m+1)(m)) ^(L) and P_(AiAi−(m+1)(m)) ^(N) are the probabilities of the pair of the arbitrary amino-acid residues A_(i) and A_(i−(m+1)) occurring in the linker sequence and the non-linker loop sequence, respectively (the order of A_(i) and A_(i−(m+1)) does not matter)); and iii) a step for obtaining the linker degree determination score F₁₁(i) of the amino acid residue Ai at the position i by the following equation: F ₁₁(i)=F ₁₁ s(i)+α₁₁ F ₁₁ p(i) (where 0≦α₁₁≦1).
 35. A method by which a linker degree determination score F₁₂(i) of an amino-acid residue Ai at a position i in an amino-acid sequence seq.0 with L₂ amino-acid residues (L₂ is an integer of 22 or more) for which the existence of n homologous sequences seq.1˜seq.n (n is an integer of 1 or more) is known is obtained by taking a window with w amino-acid residues before and after the amino-acid residue at the position i (i is an integer of 1 or more but not more than 22), the method comprising: i) a step for identifying an amino-acid residue A_(i) ^(k) in a seq.k (k is an integer of 1 or more but not more than n) corresponding to an amino-acid residue Ai⁰ at a position i in the seq.0 by aligning seq.0 and seq.1˜seq.n; ii) a step for obtaining parameters S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m) for the amino-acid residue Ai at the position i by the following equation: $S_{Ai}^{\prime} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k}} \right)/\left( {n - n_{{gap}\quad 1}} \right)}$ ${S_{{AiAi} + {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k_{{Ai} + {({m + 1})}}{k(m)}}} \right)/\left( {n - n_{{gap}\quad 2}} \right)}$ ${S_{{AiAi} - {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k_{{Ai} - {({m + 1})}}{k(m)}}} \right)/\left( {n - n_{{gap}\quad 3}} \right)}$ (where n_(gap1) is the number of gaps occurring in A_(i) ^(k), S_(Ai)k=log(P_(Ai)k^(L)/P_(Ai)k^(N)) where S_(Ai)k=0 if there is no statistically significant difference between P_(Ai)k^(L) and P_(Ak) ^(N); P_(Ai)k^(L) and P_(Ai)k^(N) are the probabilities of the amino-acid residue A_(i) ^(k) occurring in a linker sequence and a non-linker loop sequence, respectively; wherein n_(gap2) is the number of gaps occurring in A_(i) ^(k) or A_(i+(m+1)) ^(k), S_(Ai)k_(Ai+(m+1))k(m)=log(P_(Ai)k_(Ai+(m+1))k_((m)) ^(L)/P_(Ai)k_(Ai+(m+1))k_((m)) ^(N)) where S_(Ai)k_(Ai+(m+1))k_((m))=0 if there is no statistically significant difference between P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m)) ^(N); P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m)) ^(N) are the probabilities of the amino-acid residues A_(i) ^(k) and A_(i+(m+1)) ^(k) occurring in a linker sequence and a non-linker loop sequence, respectively (the order of A_(i) ^(k) and A_(i+(m+1)) ^(k) does not matter) as interrupted by m arbitrary amino-acid residues (m is an integer, m=0, 1,2); and wherein n_(gap3) is the number of gaps occurring in A_(i) ^(k) or A_(i−(m+1)) ^(k), S_(Ai)k_(Ai−(m+1))k(m)=log(P_(Ai)k_(Ai−(m+1))k_((m)) ^(L)/P_(Ai)k_(Ai−(m+1))k_((m)) ^(N)) where S_(Ai)k_(Ai−(m+1))k(m)=0 if there is no statistically significant difference between P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m)) ^(N); P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m)) ^(N) are the probabilities of the amino-acid residues A_(i) ^(k) and A_(i−(m+1)) ^(k) occurring in a linker sequence and a non-linker loop sequence, respectively (the order of A_(i) ^(k) and A_(i)−(m+1)^(k) does not matter) as interrupted by m arbitrary amino-acid residues (m is an integer, m=0, 1, 2)); iii) a step for obtaining a linker trend score F₁₂s(i) of an amino-acid residue by the following equation: ${F_{12}{s(i)}} = {\left( {\sum\limits_{k = {i - w}}^{\quad{i + w}}\quad S_{Ak}^{\prime}} \right)/W}$ iv) a step for obtaining a linker trend score F₁₂p(i) of an arbitrary amino-acid residue pair by the following equation: ${F_{12}{p(i)}} = {\sum\limits_{k = {i - w}}^{\quad{i + w}}{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{{AiAi} + {({m + 1})}}^{\prime}(m)} + {S_{{AiAi} - {({m + 1})}}^{\prime}(m)}} \right)/2}} \right)/W}}$ and v) a step for obtaining the linker degree determination score F₁₂(i) for the amino-acid residue Ai at the position i by the following equation: F ₁₂(i)=F ₁₂ s(i)+α₁₂ F ₁₂ p(i) (where 0≦α₁₂≦1).
 36. A system by which a linker degree determination score F₁₂(i) of an amino-acid residue Ai at a position i in an amino-acid sequence seq.0 with L₂ amino-acid residues (L₂ is an integer of 22 or more) for which the existence of n homologous sequences seq.1˜seq.n (n is an integer of 1 or more) is known is obtained by taking a window with w amino-acid residues before and after the amino-acid residue at the position i (i is an integer of 1 or more but not more than 22), the system comprising: i) a means for identifying an amino-acid residue A_(i) ^(k) in a seq.k (k is an integer of 1 or more but not more than n) corresponding to an amino-acid residue Ai⁰ at the position i in the seq.0 by aligning seq.0 and seq.1˜seq.n; ii) a means for obtaining parameters for the amino-acid residue Ai at the position i, S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m), by the following equation: $S_{Ai}^{\prime} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k}} \right)/\left( {n - n_{{gap}\quad 1}} \right)}$ ${S_{{AiAi} + {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k_{{Ai} + {({m + 1})}}{k(m)}}} \right)/\left( {n - n_{{gap}\quad 2}} \right)}$ ${S_{{AiAi} - {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k_{{Ai} - {({m + 1})}}{k(m)}}} \right)/\left( {n - n_{{gap}\quad 3}} \right)}$ (where n_(gap1) is the number of gaps occurring in A_(i) ^(k), S_(Ai)k=log(P_(Ai)k^(L)/P_(Ai)k^(N)) where S_(Ai)k=0 if there is no statistically significant difference between P_(Ai)k^(L) and P_(Ai)k^(N); P_(Ai)k^(L) and P_(Ai)k^(N) are the probabilities of the amino-acid residue A_(i) ^(k) occurring in a linker sequence and a non-linker loop sequence, respectively; wherein n_(gap2) is the number of gaps occurring in A_(i) ^(k) or A_(i+(m+1)) ^(k), S_(Ai)k_(Ai+(m+1))k_((m))=log(P_(Ai)k_(Ai+(m+1))k_((m)) ^(L)/P_(Ai)k_(Ai+(m+1))k_((m)) ^(N)) where S_(Ai)k_(Ai+(m+1))k_((m))=0 if there is no statistically significant difference between P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m)) ^(N); P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m)) ^(N) are the probabilities of the amino-acid residues A_(i) ^(k) and A_(i+(m+1)) ^(k) occurring in the linker sequence and the non-linker loop sequence, respectively (the order of A_(i) ^(k) and A_(i+(m+1)) ^(k) does not matter) as interrupted by m arbitrary amino-acid residues (m is an integer, m=0, 1, 2); and wherein n_(gap3) is the number of gaps occurring in A_(i) ^(k) or A_(i−(m+1)) ^(k), S_(Ai)k_(Ai−(m+1))k(m)=log(P_(Ai)k_(Ai−(m+1))k_((m)) ^(L)/P_(Ai)k_(Ai−(m+1))k_((m)) ^(N)) where S_(Ai)k_(Ai−(m+1))k_((m))=0 if there is no statistically significant difference between P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m)) ^(N); P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m)) ^(N) are the probabilities of the amino-acid residues A_(i) ^(k) and A_(i−(m+1)) ^(k) occurring in the linker sequence and the non-linker loop sequence, respectively (the order of A_(i) ^(k) and A_(i−(m+1)) ^(k) does not matter) as interrupted by m arbitrary amino acid residues (m is an integer, m=0, 1, 2)); iii) a means for obtaining a linker trend score F₁₂s(i) of an amino-acid residue by the following equation; ${F_{12}{s(i)}} = {\left( {\sum\limits_{k = {i - w}}^{\quad{i + w}}\quad S_{Ak}^{\prime}} \right)/W}$ iv) a means for obtaining a linker trend score F₁₂p(i) of an arbitrary amino-acid residue pair by the following equation; ${F_{12}{p(i)}} = {\sum\limits_{k = {i - w}}^{\quad{i + w}}{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{{AiAi} + {({m + 1})}}^{\prime}(m)} + {S_{{AiAi} - {({m + 1})}}^{\prime}(m)}} \right)/2}} \right)/W}}$ and v) a means for obtaining the linker degree determination score F₁₂(i) for the amino-acid residue Ai at the position i by the following equation: F ₁₂(i)=F ₁₂ s(i)+α₁₂ F ₁₂ p(i) (where 0≦α₁₂≦1).
 37. A program for having a computer function as a system by which a linker degree determination score F₁₂(i) of an amino-acid residue Ai at a position i in an amino-acid sequence seq.0 with L₂ amino-acid residues (L₂ is an integer of 22 or more) for which the existence of n homologous sequences seq.1˜seq.n (n is an integer of 1 or more) is known is obtained by taking a window with w amino-acid residues before and after the amino-acid residue at the position i (i is an integer of 1 or more but not more than 22), the system comprising: i) a means for identifying an amino acid residue A_(i) ^(k) in a seq.k (k is an integer of 1 or more but not more than n) corresponding to an amino-acid residue Ai⁰ at the position i in the seq.0 by aligning seq.0 and seq.1˜seq.n; ii) a means for obtaining parameters for the amino-acid residue Ai at the position i, S′_(Ai), S′_(AiAi+(m+1))(m) and S′_(AiAi−(m+1))(m), by the following equation: $S_{Ai}^{\prime} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k}} \right)/\left( {n - n_{{gap}\quad 1}} \right)}$ ${S_{{AiAi} + {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k_{{Ai} + {({m + 1})}}{k(m)}}} \right)/\left( {n - n_{{gap}\quad 2}} \right)}$ ${S_{{AiAi} - {({m + 1})}}^{\prime}(m)} = {\left( {\sum\limits_{k = 0}^{n}\quad{S_{Ai}k_{{Ai} - {({m + 1})}}{k(m)}}} \right)/\left( {n - n_{{gap}\quad 3}} \right)}$ (where n_(gap1) is the number of gaps occurring in A_(i) ^(k), S_(Ai)k=log(P_(Ai) k ^(L)/P_(Ai)k^(N)) where S_(Ai)k=0 if there is no statistically significant difference between P_(Ai)k^(L) and P_(Ai)k^(N); P_(Ai)k^(L) and P_(Ai)k^(N) are the probabilities of the amino-acid residue A_(i) ^(k) occurring in a linker sequence and a non-linker loop sequence, respectively; wherein n_(gap2) is the number of gaps occurring in A_(i) ^(k) or A_(i+(m+1)) ^(k), S_(Ai)k_(Ai+(m+1))k(m)=log(P_(Ai)k_(Ai+(m+1))k_((m)) ^(L)/P_(Ai)k_(Ai+(m+1))k_((m)) ^(N)) where S_(Ai)k_(Ai+(m+1))k_((m))=0 if there is no statistically significant difference between P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m)) ^(N); P_(Ai)k_(Ai+(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai+(m+1))k_((m)) ^(N) are the probabilities of the amino-acid residues A_(i) ^(k) and A_(i+(m+1)) ^(k) occurring in the linker sequence and the non-linker loop sequence, respectively (the order of A_(i) ^(k) and A_(i+(m+1)) ^(k) does not matter) as interrupted by m arbitrary amino-acid residues (m is an integer, m=0, 1, 2); and wherein n_(gap3) is the number of gaps occurring in A_(i) ^(k) or A_(i−(m+1)) ^(k), S_(Ai)k_(Ai−(m+1))k(m)=log(P_(Ai)k_(Ai−(m+1))k_((m)) ^(L)/P_(Ai)k_(Ai−(m+1))k_((m)) ^(N)) where S_(Ai)k_(Ai−(m+1))k_((m))=0 if there is no statistically significant difference between P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m)) ^(N); P_(Ai)k_(Ai−(m+1))k_((m)) ^(L) and P_(Ai)k_(Ai−(m+1))k_((m)) ^(N) are the probabilities of the amino-acid residues A_(i) ^(k) and A_(i−(m+1)) ^(k) occurring in the linker sequence and the non-linker loop sequence, respectively (the order of A_(i) ^(k) and A_(i−(m+1)) ^(k) does not matter) as interrupted by m arbitrary amino-acid residues (m is an integer, m=0, 1, 2); iii) a means for obtaining a linker trend score F₁₂s(i) of an amino-acid residue by the following equation; ${F_{12}{s(i)}} = {\left( {\sum\limits_{k = {i - w}}^{i + w}\quad S_{Ak}^{\prime}} \right)/W}$ iv) a means for obtaining a linker trend score F₁₂p(i) of an arbitrary amino-acid residue pair by the following equation; ${F_{12}{p(i)}} = {\sum\limits_{k = {i - w}}^{i + w}\quad{\left( {\sum\limits_{m = 0}^{2}\quad{\left( {{S_{{AiAi} + {({m + 1})}}^{\prime}(m)} + {S_{{AiAi} - {({m + 1})}}^{\prime}(m)}} \right)/2}} \right)/W}}$ and v) a means for obtaining the linker degree determination score F₁₂(i) for the amino-acid residue Ai at the position i by the following equation: F ₁₂(i)=F ₁₂ s(i)+α₁₂ F ₁₂ p(i) (where 0≦α₁₂≦1).
 38. A method of predicting a domain linker portion comprising: i) a step for obtaining a linker degree determination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) according to the method as set forth in claim 32 (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence); ii) a step for executing secondary-structure prediction on the amino acid sequence and predicting which regions will take a loop structure; iii) a step for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker degree determination score is greater than 0; and iv) a step for predicting for each of the regions obtained in iii) that the position at which the linker degree determination score takes a maximum value is the position at which the domain linker exists.
 39. A system for predicting a domain linker portion comprising: i) a means for obtaining a linker degree determination score of an amino acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) according to the method as set forth in claim 32 (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence); ii) a means for executing secondary-structure prediction on the amino-acid sequence and predicting which regions will take a loop structure; iii) a means for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker degree determination score is greater than 0; and iv) a means for predicting for each of the regions obtained in iii) that the position at which the linker degree determination score takes a maximum value is the position at which the domain linker exists.
 40. A program for having a computer function as a system for predicting a domain linker portion, the system comprising: i) a means for obtaining a linker degree determination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) according to the method as set forth in claim 32 (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence); ii) a means for executing secondary-structure prediction on the amino-acid sequence and predicting which regions will take a loop structure; iii) a means for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker degree determination score is greater than 0; and iv) a means for predicting for each of the regions obtained in iii) that the position at which the linker degree determination score takes a maximum value is the position at which the domain linker exists.
 41. A method of constructing an amino-acid sequence database comprising: i) a step for obtaining a linker degree determination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) according to the method as set forth in claim 32 (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence); ii) a step for executing secondary-structure prediction on the amino-acid sequence and predicting which regions will take a loop structure; iii) a step for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker degree determination score is greater than 0; iv) a step for selecting from the regions obtained in iii) the one whose maximum value of the linker degree determination score is greater than a lower limit value; and v) a step for recording in a recording medium the amino-acid sequence of the region selected in iv).
 42. A domain linker peptide made of the same amino-acid sequence as the amino-acid sequence of a region whose maximum value of a linker degree determination score is greater than a lower limit value, and which was obtained by a method comprising: i) a step for obtaining a linker degree determination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino acid residues (L₂ is an integer of 22 or more) according to a method as set forth in claim 32 (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino acid sequence); ii) a step for executing secondary-structure prediction on the amino-acid sequence and predicting which regions will take a loop structure; iii) a step for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker trend determination score is greater than 0; and iv) a step for selecting from the regions obtained in iii) the one whose maximum value of the linker degree determination score is greater than the lower limit value.
 43. A method of predicting a structural domain comprising a step for predicting about an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) that a sequence fragment generated by cutting off the amino-acid sequence at any portion of a region including the domain linker portion predicted by the method as set forth in claim 38 or the position at which a domain linker exists is a structural domain.
 44. A method as set forth in claim 43, wherein if n domain linker portions are predicted, t of them (t is an integer of 1 or more but not more than n) is selected, all the patterns for cutting an amino acid sequence at that position are considered, and all the sequence fragments obtained are predicted as structural domains.
 45. A system for predicting a structural domain comprising a means for predicting about an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) that a sequence fragment generated by cutting off the amino-acid sequence at any portion of a region including the domain linker portion predicted by the method as set forth in claim 38 or the position at which a domain linker exists is a structural domain.
 46. A program for having a computer function as a system for predicting a structural domain, the system comprising a means for predicting about an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) that a sequence fragment generated by cutting off the amino-acid sequence at any portion of a region including the domain linker portion predicted by the method as set forth in claim 38 or the position at which a domain linker exists is a structural domain.
 47. A method of constructing an amino-acid sequence database comprising a step in which concerning an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more), the amino-acid sequence of a sequence fragment generated by cutting off the first-mentioned amino-acid sequence at any portion of a region including the domain linker portion predicted by the method as set forth in claim 38 or the portion at which a domain linker exists is recorded in a recording medium.
 48. A method of producing a protein comprising a step for producing a protein having the same amino-acid sequence as the structural domain predicted by the method as set forth in claim
 43. 49. A method of analyzing a protein comprising a step for analyzing a protein having the same amino-acid sequence as the structural domain predicted by the method as set forth in claim
 43. 50. A method of producing a protein comprising designing a new multi-domain protein generated by connecting at least 2 protein fragments with a domain linker peptide as set forth in claim 42 and producing this multi-domain protein.
 51. A method of predicting a domain linker portion comprising: i) a step for obtaining a linker degree determination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) according to the method as set forth in claim 35 (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence); ii) a step for executing secondary-structure prediction on the amino acid sequence and predicting which regions will take a loop structure; iii) a step for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker degree determination score is greater than 0; and iv) a step for predicting for each of the regions obtained in iii) that the position at which the linker degree determination score takes a maximum value is the position at which the domain linker exists.
 52. A system for predicting a domain linker portion comprising: i) a means for obtaining a linker degree determination score of an amino acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) according to the method as set forth in claim 35 (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence); ii) a means for executing secondary-structure prediction on the amino-acid sequence and predicting which regions will take a loop structure; iii) a means for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker degree determination score is greater than 0; and iv) a means for predicting for each of the regions obtained in iii) that the position at which the linker degree determination score takes a maximum value is the position at which the domain linker exists.
 53. A program for having a computer function as a system for predicting a domain linker portion, the system comprising: i) a means for obtaining a linker degree determination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) according to the method as set forth in claim 35 (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence); ii) a means for executing secondary-structure prediction on the amino-acid sequence and predicting which regions will take a loop structure; iii) a means for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker degree determination score is greater than 0; and iv) a means for predicting for each of the regions obtained in iii) that the position at which the linker degree determination score takes a maximum value is the position at which the domain linker exists.
 54. A method of constructing an amino-acid sequence database comprising: i) a step for obtaining a linker degree determination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino-acid residues (L₂ is an integer of 22 or more) according to the method as set forth in claim 35 (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino-acid sequence); ii) a step for executing secondary-structure prediction on the amino-acid sequence and predicting which regions will take a loop structure; iii) a step for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker degree determination score is greater than 0; iv) a step for selecting from the regions obtained in iii) the one whose maximum value of the linker degree determination score is greater than a lower limit value; and v) a step for recording in a recording medium the amino-acid sequence of the region selected in iv).
 55. A domain linker peptide made of the same amino-acid sequence as the amino-acid sequence of a region whose maximum value of a linker degree determination score is greater than a lower limit value, and which was obtained by a method comprising: i) a step for obtaining a linker degree determination score of an amino-acid residue Ai at a position i in an amino-acid sequence with L₂ amino acid residues (L₂ is an integer of 22 or more) according to a method as set forth in claim 35 (however, a linker degree determination score need not be obtained for 0 to 50 residues at the N and C terminals of the amino acid sequence); ii) a step for executing secondary-structure prediction on the amino-acid sequence and predicting which regions will take a loop structure; iii) a step for obtaining regions which are found likely to take a loop structure in the secondary-structure prediction and whose linker trend determination score is greater than 0; and iv) a step for selecting from the regions obtained in iii) the one whose maximum value of the linker degree determination score is greater than the lower limit value. 